Quantum Physics, Wave Numbers & Schrodingers Equation

Hi there, my question looks like this

I need some help with the first part. I understand that if I can get k1 in terms of k2 (or even vice versa) then I would be able to do the next 3 parts quite easily but I just don't know where to start really. Any help on this is much appreicated.

Thanks

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Reply 1

noobynoo

6

Have you tried putting the values in the Shrodinger equation to get the wavelength and hence wave number in part 1.

Do this twice for x<0 and again for x>0 with the potential to see what you get. You should find that the wave numbers k_1 and k_2 satisfy the equation.

Now you've done this, try the second part. I presume this is the way to do it.

For (d) I get 989,795. What did you get? I don't know how this relates to the classical result.

(edited 9 years ago)

Reply 2

Eremor

OP

9

Original post by noobynoo

Have you tried putting the values in the Shrodinger equation to get the wavelength and hence wave number in part 1.

Do this twice for x<0 and again for x>0 with the potential to see what you get. You should find that the wave numbers k_1 and k_2 satisfy the equation.

Now you've done this, try the second part. I presume this is the way to do it.

Thing is im not really certain how to do what you say. Quite confused with how to use the schrodinger equation in general really. I certainly am unsure how I'd use it to get the wavelength and what form of the equation i need.

Reply 3

noobynoo

6

Original post by Eremor

Thing is im not really certain how to do what you say. Quite confused with how to use the schrodinger equation in general really. I certainly am unsure how I'd use it to get the wavelength and what form of the equation i need.

Well, I just used the general solution psi(x,t) = exp( ikx-iEt). Put this in the wave equation and solve for the momentum k. The momentum is proportional to the frequency and inversely proportional to the wavelength. Does this help? I'm not an expert in quantum mechanics but this seems the easiest way to do it. Or maybe you don't need that if you know:

E = (1/2m) * k^2 + U

Wave number is proportional to k.

(edited 9 years ago)

Reply 4

WishingChaff

2

To do this question first split your diagram into two regions. Region 1 will be when x<0 and region 2 will be when

x \geq 0

. Now, what is the wavefunction of the particle in these two regions, up to some constants that will be determined later?

Hint: Solve the Schrodinger equation in these two regions.

Original post by Eremor

Hi there, my question looks like this

I need some help with the first part. I understand that if I can get k1 in terms of k2 (or even vice versa) then I would be able to do the next 3 parts quite easily but I just don't know where to start really. Any help on this is much appreicated.

Thanks

Quantum Physics, Wave Numbers & Schrodingers Equation

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