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# Quantum State watch

1. Hello. I was wondering if anybody could give me a quick, reasonably simple and usable definition of a 'quantum state'? It's come up a few times in my textbook, and though I've tried to research it I couldn't find a definition I understood. For example, the Pauli Exclusion Principle does not allow fermions to exist in the same quantum state- at first I thought this meant at the same place in space and time, but this can't be true because protons and neutrons can exist in the same state. Any help appreciated, thanks.
2. In classical Physics, we can define the state of a system (ie a particle or something) using it's position and velocity (or momentum), and this completely describes where it is, and where it will be in a given amount of time.

However in quantum mechanics, we think about particles in terms of wave functions. This means that instead of having a (predetermined) fixed property (defined using 'quantum numbers') at a certain time, it could have a number of different possible properties. It is only when we observe it, that the wave function 'collapses' down to give us one particular set of measurements of its state. Furthermore each state can be at a number of different energies.

So basically, in a nutshell, a state is a just a complete description of the properties of a system. It contains information that allow us to determine the state of a system at a later time. A quantum state just means the state describes a quantum system (one obeying the laws of quantum mechanics) rather than a classical system and classical mechanics.

And with the Pauli exclusion principle - protons don't exist in the same state as other protons, and similarly with neutrons (they do obey the Pauli exclusion principle). Basically in an atom each electron, proton and neutron have a different set of quantum numbers to the other particles of the same type.

If you want me to try and explain it in a different way just ask
3. Time for my Oxford Dictionary for Physics!
Quantum State: "The state of a quantised (discrete rather than continuous values used) system as described by its quantum numbers. For instance the state of a hydrogen atom is described by the four quantum numbers:

In the ground state they have values 1, 0, 0 and 1/2 respectively."
4. (Original post by pianofluteftw)
In classical Physics, we can define the state of a system (ie a particle or something) using it's position and velocity (or momentum), and this completely describes where it is, and where it will be in a given amount of time.

However in quantum mechanics, we think about particles in terms of wave functions. This means that instead of having a (predetermined) fixed property (defined using 'quantum numbers') at a certain time, it could have a number of different possible properties. It is only when we observe it, that the wave function 'collapses' down to give us one particular set of measurements of its state. Furthermore each state can be at a number of different energies.

So basically, in a nutshell, a state is a just a complete description of the properties of a system. It contains information that allow us to determine the state of a system at a later time. A quantum state just means the state describes a quantum system (one obeying the laws of quantum mechanics) rather than a classical system and classical mechanics.

And with the Pauli exclusion principle - protons don't exist in the same state as other protons, and similarly with neutrons (they do obey the Pauli exclusion principle). Basically in an atom each electron, proton and neutron have a different set of quantum numbers to the other particles of the same type.

If you want me to try and explain it in a different way just ask
Hey thanks for the reply! I think I understand. Is it like with Feynman diagrams for the probability of a process occurring? So the electron, proton or neutron has a specific possibility of having a particular set of values, corresponding to a quantum number, depending on the number of ways that set of values can occur?
Also, with quantum states, is position a property? If it is, when an electron and a neutron (for example) share a quantum number and so can exist in the same quantum state, does that mean they can exist at the same point in space-time?
5. (Original post by Piguy)
Time for my Oxford Dictionary for Physics!
Quantum State: "The state of a quantised (discrete rather than continuous values used) system as described by its quantum numbers. For instance the state of a hydrogen atom is described by the four quantum numbers:

In the ground state they have values 1, 0, 0 and 1/2 respectively."
Cheers for the reply! Following on what pianofluteFTW explained, I assume that the quantum numbers represent specific properties of the atom? For example, the 1/2 for m_s would maybe be the spin? (Whatever that is...)
6. (Original post by Benjamin.F)
Cheers for the reply! Following on what pianofluteFTW explained, I assume that the quantum numbers represent specific properties of the atom? For example, the 1/2 for m_s would maybe be the spin? (Whatever that is...)
You're correct, but as far as my knowledge extends, the quantum numbers describe electrons inside an atom - I don't know how we use them to describe other quantum systems.

n = energy level of the electron, it describes the shell that an electron is in and can only be a natural number (any number ), so in the ground state, an electron is in the first shell and therefore has n = 1.

l = angular quantum number, and this describes the subshell that an electron is in. Each subshell has small energetic differences. The value of l can range between 0 and (n - 1). The number it is describes what subshell it is a part of, i.e. l = 0 is a s-orbital, l = 1 is a p orbital.

describes the orbital within a subshell - each orbital can only hold two electrons (this is where the Pauli exclusion principle comes in, in a second). The value of varies between and - so a p-orbital (l = 1) has 3 orbitals (-1, 0, 1) and can thus hold 6 electrons.

describes the spin (spin is a weird quantum form of angular momentum that I don't think I understand ). Due to the Pauli exclusion principle, no electron can exist in an equivalent quantum state as the other - so for an electron, . Note that other types of particles (like bosons) can have integer spins - fermions, which is what an electron is, have half-integer spins.

So say we have an electron with the quantum state 3, 1, 0, . It is the electron in the 3rd shell, in the second p orbital (called ), with a spin of 1/2.
7. (Original post by Benjamin.F)
Hey thanks for the reply! I think I understand. Is it like with Feynman diagrams for the probability of a process occurring? So the electron, proton or neutron has a specific possibility of having a particular set of values, corresponding to a quantum number, depending on the number of ways that set of values can occur?
Also, with quantum states, is position a property? If it is, when an electron and a neutron (for example) share a quantum number and so can exist in the same quantum state, does that mean they can exist at the same point in space-time?
Well as I understand it (but it all gets fairly complicated :P) most quantum properties are expressed in terms of probability - there is a chance of measuring several different states (superposition). So we then look at quantised variables, they have a restricted set of values they can be. This just means that instead of having a variable where the magnitude can be any numerical value, there are fixed values and it has to be one of them.

So for example, for electrons in an atom, with the four quantum numbers n,l,m and ms we describe the state. n refers to what energy level the electron is on (electron shell), l refers to the shape or type of orbital (each state could be in a few different shapes), m is the magnetic quantum number and therefore can kind of be seen to describe the electrons position in 3D space, and ms describes the spin of the electron (which is just a property - it's not like the electron spinning as we would imagine lets say a planet spinning, it's an intrinsic property related to angular momentum and is basically really hard to imagine :P).

So yeah, there is a certain probability an electron might be in these states, but once we have made a measurement the electron is fixed to a particular state.

Hope this makes sort of sense - you wont have to know all of this for A level Physics I don't think (but maybe in chemistry?)
8. (Original post by Hype en Ecosse)
You're correct, but as far as my knowledge extends, the quantum numbers describe electrons inside an atom - I don't know how we use them to describe other quantum systems.

n = energy level of the electron, it describes the shell that an electron is in and can only be a natural number (any number ), so in the ground state, an electron is in the first shell and therefore has n = 1.

l = angular quantum number, and this describes the subshell that an electron is in. Each subshell has small energetic differences. The value of l can range between 0 and (n - 1). The number it is describes what subshell it is a part of, i.e. l = 0 is a s-orbital, l = 1 is a p orbital.

describes the orbital within a subshell - each orbital can only hold two electrons (this is where the Pauli exclusion principle comes in, in a second). The value of varies between and describes the spin (spin is a weird quantum form of angular momentum that I don't think I understand ). Due to the Pauli exclusion principle, no electron can exist in an equivalent quantum state as the other - so for an electron, . Note that other types of particles (like bosons) can have integer spins - fermions, which is what an electron is, have half-integer spins.

So say we have an electron with the quantum state 3, 1, 0, . It is the electron in the 3rd shell, in the second p orbital (called ), with a spin of 1/2.
Thanks that's brilliant! But I'm still a bit confused about the quantum numbers. If, when unobserved, a particle can exist in a number of different quantum states at the same time, due to quantum mechanics, and each state means different quantum numbers, does that mean that, for example, each electron has a probability of being in each shell and orbital, with different spin? (Sorry for the long sentence )
9. (Original post by pianofluteftw)
Well as I understand it (but it all gets fairly complicated :P) most quantum properties are expressed in terms of probability - there is a chance of measuring several different states (superposition). So we then look at quantised variables, they have a restricted set of values they can be. This just means that instead of having a variable where the magnitude can be any numerical value, there are fixed values and it has to be one of them.

So for example, for electrons in an atom, with the four quantum numbers n,l,m and ms we describe the state. n refers to what energy level the electron is on (electron shell), l refers to the shape or type of orbital (each state could be in a few different shapes), m is the magnetic quantum number and therefore can kind of be seen to describe the electrons position in 3D space, and ms describes the spin of the electron (which is just a property - it's not like the electron spinning as we would imagine lets say a planet spinning, it's an intrinsic property related to angular momentum and is basically really hard to imagine :P).

So yeah, there is a certain probability an electron might be in these states, but once we have made a measurement the electron is fixed to a particular state.

Hope this makes sort of sense - you wont have to know all of this for A level Physics I don't think (but maybe in chemistry?)
Thank you so much! That does make sense. One last question; if the electrons cannot have the same quantum state, can they at least have some of the same quantum numbers? As in, if there are multiple possible states, the electrons must have multiple possible positions; but there are already electrons in the other orbitals and shells of the atom (most of the time). So how do all the electrons manage to have multiple, different quantum states?
10. (Original post by Benjamin.F)
Thank you so much! That does make sense. One last question; if the electrons cannot have the same quantum state, can they at least have some of the same quantum numbers? As in, if there are multiple possible states, the electrons must have multiple possible positions; but there are already electrons in the other orbitals and shells of the atom (most of the time). So how do all the electrons manage to have multiple, different quantum states?
Yep they can share quantum numbers - we know more than one electron can be in the same shell. The quantities above are related, as we kind of see it as there are the main electron shells (n), then each has a certain number of sub shells (l) and these two numbers are related - for a certain value of n, there are only a certain number of values for l. But within each sub shell, the electrons can differ in terms of orbital shape, and in terms of spin.

Looking at the most simple case, the ground state (lowest energy level), where n=1, we have to say l=0. So therefore m=0, but we can have two electrons in the ground state, one spin up, one spin down. So to answer your question, yes they can share the same quantum numbers, but have to differ on at least one - no two electrons can have exactly the same set)

(And this is why electrons fill different shells - it is as a result of quantum Physics and the Pauli exclusion principle)
11. (Original post by Benjamin.F)
Thanks that's brilliant! But I'm still a bit confused about the quantum numbers. If, when unobserved, a particle can exist in a number of different quantum states at the same time, due to quantum mechanics, and each state means different quantum numbers, does that mean that, for example, each electron has a probability of being in each shell and orbital, with different spin? (Sorry for the long sentence )
Sorry, I screwed up the LaTeX, but I just fixed it there!

I don't really understand quantum mechanics past a super, duper basic level so I can't answer your questions here!

(Original post by Benjamin.F)
Thank you so much! That does make sense. One last question; if the electrons cannot have the same quantum state, can they at least have some of the same quantum numbers? As in, if there are multiple possible states, the electrons must have multiple possible positions; but there are already electrons in the other orbitals and shells of the atom (most of the time). So how do all the electrons manage to have multiple, different quantum states?
They can have the same quantum numbers, as long as ALL of them aren't the same. e.g.

3,1,0, 1/2 and 3,1,0, -1/2 describe two electrons that are in the same py orbital. They have opposite spins - this is what prevents them being in the same quantum state.

They have lots of different quantum states simply because there's a lot of variability. I gave you the ranges there (which, I imagine, have been derived mathematically) that describes the permissive numbers depending on other variables.

n = energy level
l can be between 0 and (n - 1)
ml = between -l and l in integer steps.
ms = positive or negative one half.

Suppose n = 1; like in a hydrogen atom in ground state. Then the only possibly value for l is zero, therefore the only possible value for m_l is zero, but m_s is independent of the other states. Therefore a hydrogen atom can hold 2 electrons in its first shell/energy level.

Let's scale up to n = 2. Suddenly we have a big change:

n = 2
l = 0, 1
m_l = -1, 0, 1 for the l = 1 subshell.

Therefore 6 electrons.

Let's say we're looking at the electrons in n = 4!

n = 4
l = 0, 1, 2, 3
m_l = -3, -2, -1, 0, 1, 2, 3 in an l = 3 subshell

Therefore 14 electrons in the f orbitals (this is what you call the l = 3 subshell).

As you can see, you can have a large amount of variation within the properties of an electron in an atom.

How about the total number of electrons in a certain energy level? Well, you just have to compute all the values of l for a given n, compute all the possible ranges of m_l given the possible l's, and double that for spin.

So for n = 4, plug all the numbers through, and you have 32 electrons that can be in that one energy level. It's easy to see, then, how we can have lots and lots of electrons in an atom and not have any of them have the same quantum state.
12. (Original post by Hype en Ecosse)
Sorry, I screwed up the LaTeX, but I just fixed it there!

I don't really understand quantum mechanics past a super, duper basic level so I can't answer your questions here!

They can have the same quantum numbers, as long as ALL of them aren't the same. e.g.

3,1,0, 1/2 and 3,1,0, -1/2 describe two electrons that are in the same py orbital. They have opposite spins - this is what prevents them being in the same quantum state.

They have lots of different quantum states simply because there's a lot of variability. I gave you the ranges there (which, I imagine, have been derived mathematically) that describes the permissive numbers depending on other variables.

n = energy level
l can be between 0 and (n - 1)
ml = between -l and l in integer steps.
ms = positive or negative one half.

Suppose n = 1; like in a hydrogen atom in ground state. Then the only possibly value for l is zero, therefore the only possible value for m_l is zero, but m_s is independent of the other states. Therefore a hydrogen atom can hold 2 electrons in its first shell/energy level.

Let's scale up to n = 2. Suddenly we have a big change:

n = 2
l = 0, 1
m_l = -1, 0, 1 for the l = 1 subshell.

Therefore 6 electrons.

Let's say we're looking at the electrons in n = 4!

n = 4
l = 0, 1, 2, 3
m_l = -3, -2, -1, 0, 1, 2, 3 in an l = 3 subshell

Therefore 14 electrons in the f orbitals (this is what you call the l = 3 subshell).

As you can see, you can have a large amount of variation within the properties of an electron in an atom.

How about the total number of electrons in a certain energy level? Well, you just have to compute all the values of l for a given n, compute all the possible ranges of m_l given the possible l's, and double that for spin.

So for n = 4, plug all the numbers through, and you have 32 electrons that can be in that one energy level. It's easy to see, then, how we can have lots and lots of electrons in an atom and not have any of them have the same quantum state.
(Original post by pianofluteftw)
Yep they can share quantum numbers - we know more than one electron can be in the same shell. The quantities above are related, as we kind of see it as there are the main electron shells (n), then each has a certain number of sub shells (l) and these two numbers are related - for a certain value of n, there are only a certain number of values for l. But within each sub shell, the electrons can differ in terms of orbital shape, and in terms of spin.

Looking at the most simple case, the ground state (lowest energy level), where n=1, we have to say l=0. So therefore m=0, but we can have two electrons in the ground state, one spin up, one spin down. So to answer your question, yes they can share the same quantum numbers, but have to differ on at least one - no two electrons can have exactly the same set)

(And this is why electrons fill different shells - it is as a result of quantum Physics and the Pauli exclusion principle)

Thanks guys that's helped me so much! I really appreciate it. I know where to come when I have other questions! Cheers!

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