Physics 48 - February 15, 2008
New Solar-like System Discovered Review of Linear Algebra
Smaller Version of the Solar System Is Discovered By DENNIS OVERBYE , NY Times, February 15, 2008 Astronomers said Wednesday that they had found a miniature version o
P48 - February 6, 2008
The algebraic solution to the Harmonic Oscillator
The Harmonic Oscillator
Classical d2x F = k x = m dt 2
We assume
x = Acos ( t + )
d 2x dt
2
= 2 A cos(t + ) = 2 x
This is a solution provided =
k (the classical oscillation frequency
Physics 48, February 8, 2008
Review and finish up the Algebraic solution to the S.E. for the Harmonic oscillator.
The algebraic approach
For the Harmonic oscillator we wrote the S.E. as
1 2 p 2 + (m x ) = E 2m
[
]
We recast the Hamiltonian in terms of th
Physics 48 January 30, 2008
Apply separation of variables to the TDSE to obtain the TIDS. Consider general characteristics of the solutions to the TIDS. Solve the infinite square well.
Solving the TDSE
2 ( x, t ) h2 ( x, t ) + U ( x)( x, t ) = ih 2 t 2m
Physics 48 - February 13, 2008 (Valentines Day Eve!)
The Analytic Solution to the Schrdinger equation for the Harmonic Oscillator (cont).
The Analytic Method: (Power Series)
We began with the Schrdinger Equation
h2 d 2 ( x ) 1 + m 2 x 2 ( x ) = E ( x ) 2