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# Wave Functions help watch

1. 1) Ψ1 = sin(𝑘𝑥)
2) Ψ2 = e^𝑖𝑘𝑥 = 𝑐𝑜𝑠(𝑘𝑥) + 𝑖sin(𝑘𝑥)

For each wave function, show that they are eigenfuntions of the hamiltonian in
i) Free Space (V(x)=0).
ii) A 'flat' potential (V(x) = V)

In each case, what is the kinetic and total energy?

I've done all of it, but how do I show in each case, what is the kinetic and total energy?

Thanks!
2. (Original post by PencilPot!)
1) Ψ1 = sin(𝑘𝑥)
2) Ψ2 = e^𝑖𝑘𝑥 = 𝑐𝑜𝑠(𝑘𝑥) + 𝑖sin(𝑘𝑥)

For each wave function, show that they are eigenfuntions of the hamiltonian in
i) Free Space (V(x)=0).
ii) A 'flat' potential (V(x) = V)

In each case, what is the kinetic and total energy?

I've done all of it, but how do I show in each case, what is the kinetic and total energy?

Thanks!
What's the Hamiltonian operator in each case?
3. (Original post by alow)
What's the Hamiltonian operator in each case?
i) ħ^2k^2/2m sin(kx)

ii) sin(kx) [ħ)^2k^2/2m + V]

i) -ħ^2 i^2 k^2/2m e^ikx

ii) e^ikx [-ħ^2 i^2 k^2/2m + V]
4. (Original post by PencilPot!)
i) ħ^2k^2/2m sin(kx)

ii) sin(kx) [ħ)^2k^2/2m + V]

i) -ħ^2 i^2 k^2/2m e^ikx

ii) e^ikx [-ħ^2 i^2 k^2/2m + V]
Ignoring constants, the Scrodinger equation will be:

is the kinetic energy operator part of the Hamiltonian.

So for , how much potential energy is there?
5. (Original post by alow)
Ignoring constants, the Scrodinger equation will be:

is the kinetic energy operator part of the Hamiltonian.

So for , how much potential energy is there?
1/2?
6. (Original post by PencilPot!)
1/2?
V(x) is the potential energy operator so when it is zero the potential energy will be...
7. (Original post by alow)
V(x) is the potential energy operator so when it is zero the potential energy will be...
0
8. (Original post by PencilPot!)
0
Yep.

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