PS5 - Physics 3316, Spring 2010 Basics of Quantum Mechanics...

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Unformatted text preview: Physics 3316, Spring 2010 Basics of Quantum Mechanics Problem Set 5 (Due in lecture, March 03, 2010) Required Readings : • French and Taylor Ch. 3, Griffiths Ch. 2 Key concepts: Manipulation of quantum operators, Properties of quantum operators (Linearity, Hermi- tian operators), Time dependent Schr¨odinger equation, square well potential. 1 An angular momentum operator Consider the wavefunctions ψ ( θ ) of the angular variable θ , restricted to the interval − π ≤ θ ≤ π . If the wavefunctions satisfy the condition ψ ( π ) = ψ ( − π ), show that the operator ˆ L = planckover2pi1 i ∂ ∂θ (1) has a real expectation value. Is this operator Hermitian? 2 Time dependence of expectation values In this problem, you will re-derive the general expression for the time dependence of the expectation values of physical observables that was discussed in lecture. The key concepts here are that the time derivative of any physical observable depends only on the TDSE and the fact that the Hamiltonian operator, being associated...
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This note was uploaded on 03/29/2010 for the course PHYS 3318 taught by Professor Flanagan during the Spring '08 term at Cornell.

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PS5 - Physics 3316, Spring 2010 Basics of Quantum Mechanics...

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