HW4 - Quantum Mechanics I Physics 3143 Assignment 4 Fall...

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Quantum Mechanics I, Physics 3143: Assignment 4, Fall 2010 1. (a) Substitute Ψ( x, t ) = Ae - λx 2 e - iωt/ 2 into the time dependent Schrodinger equation for a particle of mass m , and determine for which potential V ( x ) and which value of λ it is a stationary state. (b) What is the energy eigenvalue of the stationary state in part (a) ? (c) What is the standard deviation (uncertainty) in position for a particle in the stationary state. ( Do it by inspection! ) Calculate the value of the uncertainty in microns if the particle is an atom of 23 Na and ω = 50s - 1 . ( Note: 1 amu 1 . 66 × 10 - 27 kg.) 2. Griffiths problem 2.11 p. 50 3. Griffiths problem 2.12 p. 50 ( Read example 2.5 before you answer
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