Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 4, Problem 4.75P
To determine

Show that φ(t)=12πeinϕeif(t) is a solution of time dependent Schrodinger equation.

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Assume MKS units... Let Q be an open subset of R³. Let B: :Q - R³ be a continuous vector .field, representing a magnetic field in 3-D space. 7 Let P be a particle with charge q E R and mass m > 0. If p is at position (x. y, z) in Q and R³ is the velocity of p, at time t, then p feels a force 7(7,7) given by - 7(7,J) := q V × B (7) . Suppose that p moves along a curve C as time t varies from a to b, and that p has position vector (t) and instantaneous velocity (t) at time t. ř (1) Explain why the two vectors 7'(t) × È(7(t)) and 7'(t) are perpen- dicular at every time t = [a, b]. (2) Using Part (1), calculate W := the work done on the particle p by the force as p moves from D = 7(a) to E = √ (b) along C. F (3) Prove that ((t)||²)=27' (t) • F(t), at each time t. (4) Using Parts (2) and (3), and Newton's Second Law, prove that if the magnetic force - ₹(7,7) is the total force on p at every time t, then p moves along C at a constant speed. dt
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