Quantum Mechanics
General solutions
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Notes
1
Introduction
2
Concepts from classical mechanics
3
The Schrödinger equation
4
Bound states of the square well
5
Infinite well
6
Scattering from potential steps and square barriers, etc.
7
The Harmonic oscillator
8
The formalism underlying QM
9
Ladder operators
10
Time dependent wave functions
11
3D Schrödinger equation
11.1
The momentum operator as a vector
11.2
Spherical coordinates
11.3
Solutions independent of
𝜃
and
φ
11.4
The hydrogen atom
11.5
Now where does the probability peak?
11.6
Spherical harmonics
11.7
General solutions
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11.7
General solutions
One of the reasons for playing such game is that we can rewrite the kinetic energy as
−
ℏ
2
2
m
p
̂
2
f
(
r
)
=
−
ℏ
2
2
m
1
r
2
∂
∂
r
r
2
∂
∂
r
f
(
r
)
+
1
r
2
L
̂
2
f
(
r
)
.
(11.34)
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