Q3: A linear harmonic oscillator is in a state which is a superposition of the ground state and the first excited state. Write an expression for the wave function real, positive coefficients if the average energy 1.4ħw.

Q3: A linear harmonic oscillator is in a state which is a superposition of the ground state and the first excited state. Write an expression for the wave function real, positive coefficients if the average energy 1.4ħw.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Connection formulae for WKB approximation

In quantum mechanics, Schrödinger’s equation for certain systems with varying parameters cannot be solved directly. In such a case, an approximation method is used to obtain the approximate solution. WKB method is a special technique used to obtain the approximate solution for Schrödinger’s time-independent equation. In general, the WKB method is used to solve linear differential equations with varying coefficients. This method is called semiclassical approximation in quantum mechanics.

Question

Q3: A linear harmonic oscillator is in a state which is a superposition of the ground state and the first
excited state. Write an expression for the wave function real, positive coefficients if the average energy
1.4ħw.

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Step 1: Discuss about simple harmonic oscillator wavefunction

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Step 2: Determine the normalized condition

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Step 3: Calculate the average energy of oscillator

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Step 4: Determine the wavefunction of oscillator

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Connection Formulae for WKB approximation

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