Physics 342
Lecture 3
Linear Transformations
Lecture 3
Physics 342
Quantum Mechanics I
Friday, January 29th, 2010
We nish up the linear algebra section by making some observations about
transformations (matrices) and decompositions (diagonalization) that
Physics 342
Lecture 12
Free Particle Comparison
Lecture 12
Physics 342
Quantum Mechanics I
Friday, February 19th, 2010
Here, we will compare our solutions so far (harmonic potential, innite
square well) with the free particle solution. There are three pro
Physics 342
Lecture 14
Piecewise Potentials I
Lecture 14
Physics 342
Quantum Mechanics I
Wednesday, February 24th, 2010
We saw that the Dirac delta potential admits a single bound state and a
continuum of scattering states. Technically, we can make any po
Physics 342
Lecture 13
Bound and Scattering Solutions for a Delta
Potential
Lecture 13
Physics 342
Quantum Mechanics I
Monday, February 22nd, 2010
We understand that free particle solutions are meant to be combined into
some sort of localized wave-packet.
Physics 342
Lecture 11
Energy and Free Particles
Lecture 11
Physics 342
Quantum Mechanics I
Wednesday, February 17th, 2010
We begin with a partition of energies classically, we can have particles
bound together in a potential well formed by their interact
Physics 342
Lecture 1
Separation of Variables
Lecture 1
Physics 342
Quantum Mechanics I
Monday, January 25th, 2010
There are three basic mathematical tools we need, and then we can begin
working on the physical implications of Schrdingers equation, which
Physics 342
Lecture 9
Harmonic Oscillator Physics
Lecture 9
Physics 342
Quantum Mechanics I
Friday, February 12th, 2010
For the harmonic oscillator potential in the time-independent Schrdinger
o
equation:
1
d2 (x)
2
+ m2 2 x2 (x) = E (x),
(9.1)
2m
dx2
we
Physics 342
Lecture 6
The Innite Square Well
Lecture 6
Physics 342
Quantum Mechanics I
Friday, February 5th, 2010
With the equation in hand, we move to simple solutions. For a particle
conned to a box, we nd that the boundary conditions impose energy
quan
Physics 342
Lecture 2
Linear Algebra I
Lecture 2
Physics 342
Quantum Mechanics I
Wednesday, January 27th, 2010
From separation of variables, we move to linear algebra. Roughly speaking,
this is the study of vector spaces and operations on vector spaces. O
Physics 342
Lecture 10
The Harmonic Oscillator III
Lecture 10
Physics 342
Quantum Mechanics I
Monday, February 15th, 2010
Today, we will nish our discussion of the harmonic oscillator. Our model
is a massive particle in an innite potential well, and we cu
Physics 342
Lecture 8
Harmonic Oscillator I
Lecture 8
Physics 342
Quantum Mechanics I
Wednesday, February 10th, 2010
We can manipulate operators, to a certain extent, as we would algebraic
expressions. By considering a factorization of the Hamiltonian, it
Physics 342
Lecture 4
Probability Density
Lecture 4
Physics 342
Quantum Mechanics I
Monday, February 1st, 2010
We review the basic notions of probability, in particular the role of probability density in determining the fundamental quantities relevant to
Physics 342
Lecture 5
Schrdingers Equation
o
Lecture 5
Physics 342
Quantum Mechanics I
Wednesday, February 3rd, 2010
Today we discuss Schrdingers equation and show that it supports the basic
o
interpretation of the fundamental object of study in quantum m
Physics 342
Lecture 7
The Innite Square Well II
Lecture 7
Physics 342
Quantum Mechanics I
Monday, February 8th, 2010
We will review some general properties of stationary states in quantum
mechanics using the innite square well solution as our vehicle. In
Physics 342
Lecture 15
Piecewise Potentials II
Lecture 15
Physics 342
Quantum Mechanics I
Friday, February 26th, 2010
We have seen a few dierent types of behavior for the stationary states
of piecewise potentials we can have oscillatory solutions on one o