PHYS 342
Fall 2011
Lecture 13:
Schrödinger’s Equation in 2 dimensions
Schrödinger s Equation in 2 dimensions
Ron Reifenberger
Birck Nanotechnology Center
Purdue University
Lecture 13
1

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F
d
mi
l s st m
th
xists
f
ti
Ψ
th t is
If we know the wavefunction, we know
everything it is possible to know
For every dynamical system, there exists a wavefunction
that is a
continuous, square-integrable*, single-valued function of the coordinates
of all the particles
and of time. If you know
Ψ
, all possible predictions
about the physical properties of the system can be obtained.
“The coordinates of all the particles”?
x
F
i
l
ti
l
i
di
i
For a single particle moving in one dimension:
,
x t
For a single particle in one dimension:
For a single particle moving in three dimensions:
,
t
r
For a single particle in a superposition of
two
quantum states, a and b:
,
( , )
( , )
a
b
x t
A
x t
B
x t
For
two
particles moving in three dimensions:
1
2
,
,
t
r r
*
Square-integrable means that the normalization integral is finite
2