Quantum Mechanics I_ 2nd Exam: Solutions (2008 fall)
1. For a particle moving under a one-dimensional potential V(x), show that any two
bounded states 1 and 2 are orthogonal, based on the time-independent Schrdinger
equation.
Solutions:
If 1 and 2 are two
Quantum Mechanics I: 1st Exam Solutions (Fall 2008)
Name_, Panther ID _
1. To understand atomic energy levels, de Broglie hypothesized that all allowed orbits for
an electron in a hydrogen atom are given by the condition that an integral number n de
Brogl
Homework 8
ADDITIONAL PROBLEM SOLUTION:
The Schrdinger equation is
2
d2
V0 ( x a ) = E
2m dx 2
For a bound state, E < 0, so that we assume that
= 2mE /
and the Schrdinger equation becomes
" 2 +
2mV0
2
( x a ) = 0 -(1)
The jump condition at x = a is gi
3. One major difference between classical and quantum mechanics on a harmonic
oscillator is that in quantum mechanics you may find probability of the particle
until x , while in classical mechanics the particle can only be in so-called
1
classical range x