- #1
Darrenm95
- 7
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Homework Statement
A particle with mass m and electric charge e is confined to move in one dimension along the x -axis. It experiences the following potential:
##V(x) = {\infty}## for ## x{\lt0}##
##V(x) = -e^2/4\pi\epsilon_0x## for ## x \geq 0 ##
(Note: the way the question is written down features no parentheses around ##4\pi\epsilon_0x##
a) Describe the potential experienced by the particle.
b) (This question just asks to write down the TISE which I can do).
c)For the region ## x \geq 0 ##, by substituting in the Schrödinger equation, show that the wave function
## u(x)= Cxexp(\text{-}\alpha x) ##
can be a satisfactory solution of the Schrodinger equation so long as the constant ##\alpha## is suitably chosen. Determine the unique expression for ##\alpha## in terms of m , e and other fundamental constants. Note that C is a normalisation constant.
Homework Equations
TISE
The Attempt at a Solution
For a) I am unsure to what the potential actually is and for c) I took the second derivative of u(x) and substituted it into the Schrodinger equation but it was more of a stab in the dark then anything else. I also thought about using boundary conditions to find an equation for ##\alpha## but given that my only boundary condition is 0, I've not managed to figure out a way of finding anything meaningful from doing this.
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