Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 4, Problem 33E
To determine

The function ψ(x,t)=Acos(kxωt) when plugged in the Schrödinger equation the result are not possibly hold for all value of x and t .

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Given that at time t = 0 a particle’s wave function is given by ψ(x, 0) =Ax/a, if 0 ≤ x ≤ a,A(b − x)/(b − a), if a ≤ x ≤ b, with A0, Otherwise.a and b as constants, answer the following questions; a) Find the normalization constant A in terms of the constants a and b. b) Sketch ψ(x, 0) as a function of x. c) Where is the particle most likely to be found at time t = 0? d) What is the probability of finding the particle to the left of a?
A particle confined in a one-dimensional box of length L(0<=x<=L) is in a state described by the wavefunction Ψ(x)= Ψ1+ Ψ2(x). Where A and B are constants given by real numbers and A>=0.(With X=6 and Y=3)l)Determine what relationship A and B must satisfy for the wavefunction to be normalized.ll)Suppose that A=B .What is the probability of the particle being found in the interval 0<=x<=L/2?lll)What values ​​of A and B that minimize the probability of finding the particle in the range of positions 0<=x<=L/2?
The normalised wavefunction for an electron in an infinite 1D potential well of length 80 pm can be written:ψ=(0.587 ψ2)+(0.277 i ψ7)+(g ψ6). As the individual wavefunctions are orthonormal, use your knowledge to work out |g|, and hence find the expectation value for the energy of the particle, in eV.
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