problems5

# problems5 - Physics 4021 Introduction to Quantum Mechanics...

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Unformatted text preview: Physics 4021: Introduction to Quantum Mechanics I Homework Assignment 5 Due in class: Thursday, Oct. 11, 2007 1. Problem 2.25. Following identities might be useful: ) ( ) ( ) ( ) ( / |) (| x x f x x f dx x df − − ′ − ′ = θ θ 1 ) ( ) ( = − + x x θ θ ) ( ) ( ) ( ) ( x f x x f δ δ = 2. Consider a particle of mass m moving in one dimension and subject to the potential ), ( ) ( , ) ( > − = < ∞ = x a x x V x x V δ α where a , α > 0. For x > a and energy E >0 the wave function may be written with two positive real numbers A and B such that ) ( ) ( k i ikx ikx Be Ae x φ ψ + − − = (a) Find the relation between k and E . (b) Due to the infinite barrier at x < 0, this wavefunction represent a total reflection of incident wave. Considering the conservation of probability current as , find the relation between A and B . ∞ → x (c) Information about the scattering is contained in the phase shift φ ( k ), which depends on the wavenumber k as we discussed in class. Please determine as we discussed in class....
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problems5 - Physics 4021 Introduction to Quantum Mechanics...

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