Infinite potential barrier


by frankcastle
Tags: barrier, infinite, potential
frankcastle
frankcastle is offline
#1
Dec18-08, 09:22 AM
P: 10
1. The problem statement, all variables and given/known data

write the solutions to the S.E in regions x<o and x between o and a

[IMG]C:\Users\karthik\Desktop[/IMG]


2. Relevant equations

I believe psi(x)= e^ikx+Re^-ikx in x<0
and psi(x)=Ae^iqx+Be^-iqx for x b/w o and a.

3. The attempt at a solution
My question is, since there is complete reflection occuring at x=a, can A=B in region x b/w 0 and a? If so, there will be destructive interference in the region, giving R=1, which is what we are asked to prove in the question. Is this approach of equating coefficients of wave traveling in +-x directions in this region applicable?
Phys.Org News Partner Science news on Phys.org
Review: With Galaxy S5, Samsung proves less can be more
Making graphene in your kitchen
Study casts doubt on climate benefit of biofuels from corn residue
buffordboy23
buffordboy23 is offline
#2
Dec18-08, 12:43 PM
P: 540
You haven't defined your potential over the domain of x. My guess based on the info given is that the potential V(x) = infinity for regions less than or equal to x = 0 and greater than or equal to x = a.

To solve for the equations, you must impart the boundary conditions on the general solution for the wave function. So, psi(x) must vanish at x = 0 and x = a. For example, suppose that psi(x) = Asin(kx) + Bcos(kx) is a general solution to the time-independent schrodinger equation. Now, for the potential I expressed in the first paragraph, we must have psi(x) = 0 at x = 0 and x = a. When x = 0, psi(x = 0) = B; therefore choose B = 0, and now psi(x) = Asin(kx). Now fit the wavefunction to x = a: psi(x=a) = 0 = Asin(ka). Under what conditions for k (the angular wavenumber) will the sine term vanish?

You can apply this idea to your solutions. As a check, verify that your solution satisfies the time-independent schrodinger equation.


Register to reply

Related Discussions
Infinite potential barrier Q Quantum Physics 4
Barrier potential with N steps...(and she's climbing the potential stariway to la...) Advanced Physics Homework 0
infinite potential barrier Advanced Physics Homework 1
Infinite potential barrier Quantum Physics 8