Q1- Check to see whether the simple linear combination (x,t) = Asin(kx -wt) - iA Bcos(kx - wt) satisfiesthe time-dependent Schrödinger equation for a free particle (V = 0).Q2-A particle in an infinite square well potential with x=0 and x-L is in the n=2 state.a) Draw the wave function of the particle.b) Find the probability that the particle is located between x=L/2 and x=3L/4.1

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Answered: Q1- Check to see whether the simple…

Q1- Check to see whether the simple linear combination (x,t) = Asin(kx -wt) - iA Bcos(kx - wt) satisfies the time-dependent Schrödinger equation for a free particle (V = 0).

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter40: Quantum Mechanics

Section: Chapter Questions

Problem 47CP

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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.

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Q1- Check to see whether the simple linear combination (x,t) = Asin(kx -wt) - iA Bcos(kx - wt) satisfies
the time-dependent Schrödinger equation for a free particle (V = 0).
Q2-A particle in an infinite square well potential with x=0 and x-L is in the n=2 state.
a) Draw the wave function of the particle.
b) Find the probability that the particle is located between x=L/2 and x=3L/4.
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