The harmonic oscillator 4, (x) wavefuction is given below. a) Use this function to calculate the average potential energy of an oscillating system. b) Show that the average potential energy is half of the total energy of this system. 1/4 x e¬ax²/2 where a = 4a W, (x) = () |kµ /h

The harmonic oscillator 4, (x) wavefuction is given below. a) Use this function to calculate the average potential energy of an oscillating system. b) Show that the average potential energy is half of the total energy of this system. 1/4 x e¬ax²/2 where a = 4a W, (x) = () |kµ /h

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter6: Quantum Mechanics In One Dimension

Section: Chapter Questions

Problem 5P

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Concept explainers

Equation of Waves

Wave is an oscillation or disturbance traveling in a medium. It performs the transportation of energy but does not carry any matter. This motion of waves will transport fuel in a medium without permanent transfer of mass (particle).

Question

h= 6.626x1034 J.s c=2.998x108 m.s1 1 eV = 1.6022x10-19 J 1Å = 1010 m,
1/2
S° xte-ax²
6
dx =
8a2
16
me =9.109x10 31 kg, k= 1.3807x10 23 J/K
Baz ) S" sin³0 d® =-
15

The harmonic oscillator Y, (x) wavefuction is given below.
a) Use this function to calculate the average potential energy of an oscillating system.
b) Show that the average potential energy is half of the total energy of this system.
v,(x) = ()*
(4q³\1/4
xe-ax? /2 where a = Jkµ /ħ

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