Infinite square well, dimensionless Hamiltonian..

[Cocoleia]

Homework Statement

Electron with mass m* moves in a 1D quantum well with infinite barriers at x= -b/2 and
x=+b/2.
Assume mass of the electron to be m*=0.5 m where “m” is free electron mass.
a. Write Schrodinger equation and the Hamiltonian in dimensionless form
b. Solve stationary Schrodinger equation, find allowed energy levels, give explicit expression for 1st,2nd, and 3rd energy levels
d. give wavefunctions for the first three levels – plot them.
e. give 3 energy levels ,in meV, for a=4 nm

Relevant Equations

H phi = -hbar^2 / 2m d^2/dx phi(x) = E phi (x)

I have always seen this problem formulated in a well that goes from 0 to L

I am confused how to use this boundary, as well as unsure of what a dimensionless hamiltonian is.
This is as far as I have gotten

 

[Paul Colby]

What would keep you from solving it as if the well was from 0 to $b$ and then, once you had the solution, changing variables $x' = x-\frac{b}{2}$?

 

[Abhishek11235]

Alternatively,put the boundary conditions at -b/2 and b/2 same as you did for [0,L]