probability of finding a particle

i so dont get this at all

the relationship between probability and amplitude^2

i cant imagine a particle with amplitude o.O i can only imagine it was a dot xD

Reply 1

ptptaylor

It's all part of the quantum theory.
I believe it was said by a famous physician
'if you understand it, you don't!' or words to that effect...

Reply 2

ixivxivi

Chaoslord

i so dont get this at all

the relationship between probability and amplitude^2

i cant imagine a particle with amplitude o.O i can only imagine it was a dot xD

Right, first off, this is going to be supremely dodgey because I am a biochemist and hence not proper :smile:

.

Basically, waves and particles do not have the traditional, classical properties that we automatically (or a least Newton) would give them - eg. that particles have a well defined mass, exist only at a single location and can have an energy of any value; and that waves have no mass, no location (will carry on to infinity unless stopped) and again can have any energy.

However, apparently (according to quantum physics, and general observation) this is not so - waves have mass (eg = the gravitation field of the sun bends light from the stars = the light waves have mass). Equally, particles can have wave-like properties - for instance if you put a beam of electrons/neutrons or even fullerenes (aka 'buckyballs') through a grating, you get a diffraction pattern very similar to that which you would get if you shone a light wave through the grating. This indicates that particles exhibit interference, a wave-like behaviour.

Hence we can't think of waves and particles in the classical sense, because it is not true. So we can think of either as 'wave-packets'.

And, I think your question refers to Heisenburg's uncertainty principle, which is one of the consequences of this 'wave-packet' nature of matter. I've been taught a reasoning behind it, but I do suspect that it's a watered down for maths-allergic biochem students version... A pure wave wll have a perfectly defined wavelength (and so an exact energy, since E = h ν = hc/&#955 :wink:

, but an entirely undefined postion (it has no position). A classical particle will have a perfectly defined postion but no definable wavelength, hence an undefined energy. However, the real wave-packets are neither classical waves or classical particles, and so have neither their energy (what I suspect you mean by 'amplitude' :smile:

) or position entirely defined. The above explanation is all very waffle-filled, and if there's any proper physics people out there, they should feel free to correct :smile:

.

The statement of Heisenburg's uncertainty principle is: 'It is impossible tospecify enrgy and postion simultaneously,with arbitary precision'
or: uncertainty in momentum times uncertainty in position is more than or equal to planck's constant divided by (2 times pi) ('h-bar') divided by 2 (you can find this less awkwardly expressed on wikipedia).

Reply 3

ixivxivi

Oh, and I know it's hard to imagine particles and waves not being like we know them in the macro, every day world, but I think you have to just accept that they are just simply different to anything we're going to know and take their properties to be what the evidence tells us they are.

Reply 4

wizz_kid

ptptaylor

It's all part of the quantum theory.
I believe it was said by a famous physician
'if you understand it, you don't!' or words to that effect...

u mean physicist?

Reply 5

Kyle_S-C

The fact is that the wavefunction of the particle (which is where you get your amplitude from) has no physical meaning whatsoever, besides the fact that the square of the wavefunction gives you the probability distribution. ixivxivi has explained the whole matter of particle-wave duality pretty well, so essentially you have to find out about wavefunctions to understand the relationship.