This course is:
• Fun!
– The ideas are presented in a way that makes a LOT more sense than a usual
QM course
– Focus on understanding one exemplar experiment in detail – you will
understand it well
– The simulation is pretty neat and allows you to relate the math to ‘real’
measurements
• Hard!
– New notation and language
– New math (hopefully not bad thanks to a great preface)
– Ideas that take some getting used to!
• Suggestions:
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Make a vocabulary list – each bolded term in the text is a good place to start
Make a list of symbols and what they mean
Write the postulates in your own words with examples and explanations
Draw diagrams for any situation which is at first unclear to you
Do/repeat calculations to get practice
Goals:
• Understand the 6 postulates of quantum
mechanics (QM) and the nature of QM
• Proficiently use matrix mechanics in the context
of QM
• You will be able to solve 4 fundamental types of
problems – each done in detail within a specific
context, then generalized to any system:
– Sequential Stern-Gerlach measurements
• Analyze generic QM problems using matrix
mechanics
– Use time evolution to understand spin precession
• Analyze generic time dependent QM problems
using matrix mechanics
Postulates of QM
•What is a postulate?
•To assume or claim as true, existent, or necessary (from MerriamWebster)
•Tell us how to treat a QM system
•Successful and tested ideas
•Can not be proven
•Accepted as accurate but would need to be re-evaluated if new
results contradicted them
•6 main postulates
•Right now they have limited meaning
•Given so you know where we are headed and connect to preface
math
6 main postulates (and examples)
1.
2.
3.
4.
5.
6.
states are defined by kets: |+>, |->
Operators are matrices: H, S…
We measure eigenvalues: +/- h/2
Probability is found by: |<+|psi>|2
States “reduce” (collapse) |psi> goes to |+>
Schrodinger equation gives time evolution,
for instance, Larmor precession