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For a quantum particle described by a wave function ψ ( x ), the expectation value of a physical quantity f ( x ) associated with the particle is defined by

 

For a particle in an infinitely deep one-dimensional box extending from x=0 to x=L, Show that

 

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Vikas
VikasLv10
26 Dec 2020

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

1. Consider a particle of mass m in a one- dimensional box -L< x < +L as shown below.
The potential of the system is given as
0 -L < x < +L
V =
8 x <-L and x > +L
(a) Determine the energy eigenvalue of the particle.
(b) Show that the expectation value of the momentum

= 0.
(c) Determine the expectation value of the kinetic energy .
(d) What is the energy eigen values if the boundary of thebox
is shifted to -L < x < +L/2

A particle of mass m is bound in a finite one-dimensional squarewell described by the potential energy function: V(x)=0 for x<a(region I)
=-v0 for -a<=x<=a (region II) with v0>0
=0 for x>a (region III)
The energy of the particle has some definite negative value-v0<E1<0.
Consider the time independent Schrodinger equation.
Question: In each of the three regions write the normalizablespatial wave function f(x) of the particle assuming that f is aneven function of x, i.e. f(x)=f(-x) and calculate the constants inyour function that are determined by the given quantities.

Please help on problem below, thank you

Consider a quantum mechanical particle-in-a-box problem with thepotential energy shown below.

For each region, assume the waveform has energy of either 0.2eVor 0.6 eV and complete the following table. For “Description of thewavefunction,” choose from the following:

I) Zero: Ψ(x) = 0

II) Standing wave: Ψ(x) = Asin(kx) + Bcos(kx)

III) Free particle plane wave propagating in the +x direction :Ψ(x) = Aexp(ikx)

IV) Free particle plane wave propagating in the -x direction :Ψ(x) = Bexp(-ikx)

V) Free particle plane waves propagating in both directions:Ψ(x) = Aexp (ikx)+ Bexp(-ikx)

VI) Exponentially decaying tunneling wave function: Ψ(x) =Aexp(-ϰx)

VII) Exponentially growing tunneling wave function: Ψ(x) =Bexp(ϰx)

VIII) Both exponentially decaying and growing tunneling wavefunctions : Ψ(x) = Aexp(-ϰx)+ Bexp(ϰx)


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