PHYS 3320
Week 2
Tutorial
– Wave functions and probability
Goals this week
:
1.
Developing intuition about the time dependence, and complex nature of, the
spatial wave function, including stationary states and superposition states (LG:
Math/phys connection, checking)
2.
Visualization of

ψ
2
, including: it is real, normalized, carries information about
location of particle (LG: Visualization)
3.
Interpretation of matrix elements, and their time dependence (LG: Math/phys
connection, checking solutions)
4.
Intuition about <x>, <x
2
>, and
σ
for simple spatial distributions (including value,
and time dependence, and fact that <x> is not necessarily "where the particle is
likely to be")
(LG: Math/phys, checking)
5.
First pass at developing intuition about "probability current" (LG: Math/phys,
building on earlier work)
Tutorial Summary
:
Students consider the time dependence of
ψ
, 
ψ

2
, <x>, and
σ
for
stationary states, superposition states, and simple "wave packet" 1D situations. This is
their first encounter with the idea that overall complex phase is not physical, but relative
complex phase can result in "sloshing". We are developing an intuition of the physical
meaning of <x>, and
σ.
This is also a first pass at developing an intuition about
"probability current" by establishing an analogy with 1D electrical current.
Reflection after administering the tutorial
We were impressed at how difficult such a simple Tutorial was. This is normally the case
with Tutorials, and perhaps one of their greatest benefits for