Consider the Time Independent Schrödinger equation for a free particle, i.e. V (x)= 0: h? d'y(x) _ Ew (x) 2m dx where m is the mass of the particle and E is its energy. Show that if we require y (x) not to diverge at xto then E cannot be negative. Hint: In order to prove this statement, assume that E<0 and rewrite (1) as: d'y(x), 2m|E| = k² w (x) where dx? and use the fact that the solutions to this equation are of the form y (x)= Ae÷*

Consider the Time Independent Schrödinger equation for a free particle, i.e. V (x)= 0: h? d'y(x) _ Ew (x) 2m dx where m is the mass of the particle and E is its energy. Show that if we require y (x) not to diverge at xto then E cannot be negative. Hint: In order to prove this statement, assume that E<0 and rewrite (1) as: d'y(x), 2m|E| = k² w (x) where dx? and use the fact that the solutions to this equation are of the form y (x)= Ae÷*

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Quantum Physics

Section: Chapter Questions

Problem 32P

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