Homework #6 Due on April 17 Problems 3.5, 3.7, 3.13, 3.14, 3.27, and 3.37. Answers: 3.5
3.27
(c) Total probability of getting
is
3.37
Homework 6 Page 1
Lecture 2
Sunday, February 17, 2008 6:27 PM
Summary:
From our previous results
Physically realizable states correspond to the square-integrable solutions of the Schrdinger equation. If we normalize the wave function at time t=0, it will stay normalized. S
Lecture 12. Problem solving
Problem 1
A particle of mass m is in the ground state (n=1) of the infinite square well:
otherwise
Solutions:
Suddenly the well expands to twice its original size - the right wall moving from a to 2a leaving
the wave function (
Lecture 13 The finite square well
Bound states Step 1: Solve Schrdinger equation for all regions
Lecture 13 Page 1
L13.P2
Step 2: Apply boundary conditions that and .
and
are continuous at
Note: V (x) is even wave functions are either even or odd. Therefo
Lecture #18 The radial equation The angular part of the wave function is the same for all spherically symmetric potentials. To solve the radial equation, we need the know V(r).
To simplify this equation, we change variables
Lecture 18 Page 1
L18.P2
This e
Lecture #17
Quantum mechanics in three dimensions
Schrdinger equation in spherical coordinates How do we generalize Schrdinger equation to three dimensions?
Hamiltonian in 3D is (from classical energy)
We previously used Thus,
Therefore, Schrdinger equati
Homework #10 Due on May 15 Problems 4.27, 4.29, 4.31, 4.49, and 4.52. Answers: 4.27
4.29
4.31
There are three states:
Homework 10 Page 1
H10 4.49
with probability with probability
with probability with probability with probability with probability
4.52
Hi
Homework #7 Due on April 24. Problems 3.22, 3.23 (don't need to normalize functions), 4.1, 4.2, and 4.3. Answers: 3.22 (c)
3.23
Eigenvalues are Looking for eigenvectors in the form yields eigenvectors
4.2
Hint: look for solutions in the form
Hint: look fo
Lecture 4
The infinite square well
otherwise
A particle in this potential is completely free, except at the two ends, where an infinite force prevents it from escaping. Let's solve the Schrdinger equation!
First, we seek stationary states
We need to solve