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1. For one particle three-dimensional system, what is the [[x,H],x)? value of
. The wave function for a one-dimensional system of mass m is ?(x) = Aexp(Lx). What is the energy for this wave function? A) ?fKh/202/2m B) -B(h/2?)2/2m D) -B2(h/21)2/2m What are the degeneracies of the first, second, and third energy levels (respectively) for a particle in a three-dimensional box? A) 1, 2, 3 B) 1, 3, 1 C) 1, 3, 3 D) 1, 2, 2 E) Cannot be determined
2. (a) Are the eigenfunctions of H for the particle in the one-dimensional box also eigenfunctions of the position operator ? (b) Calculate the average value of x for the case where n 4. Explain your result by comparing it with what you would expect for a classical particle. Repeat your calculation for n = 6 and, from these two results, suggest an expression valid for all values of n. How does your result compare with the prediction based on...
for a one-dimensional particle in a box, of the potential at x=+c is infinity, then the wave function at x=+c must be For a one-dimensional particle in a box, if the potential at x = +c is infinity, then the wavefunction at x = +c must be a. O b. a positive number less than 1 O c. a positive number greater than 1 d. 1
for a one-dimensional particle in a box, of the potential at x=+c is infinity, then the wave function at x=+c must be For a one-dimensional particle in a box, if the potential at x = +c is infinity, then the wavefunction at x = +c must be a. O b. a positive number less than 1 O c. a positive number greater than 1 d. 1
nh 61. The energy for one-dimensional particle-in-a-box is E=" 1. For a particle in a 0 three-dimensional cubic box (Lx=Ly=L2), if an energy level has twice the energy of the ground state, what is the degeneracy of this energy level? (B) 1 (C)2 (D) 3 (E) 4 (A) 0
Particle in a three-dimensional box: a. Give the equation for a particle in a three-dimensional box b. How does the density of states (i.e., number of states per unit of energy) change with increasing energy? Explain the answer.
A one-dimensional particle of mass m is confined within the region 0 < x < a and wave function V(x, t) = sin(TI)e-iwt. a Given the wave function 1(x, t) above, show that V is independent of t. b Calculate the probability of finding the particle in the interval a 5 x 54
for a one dimensional particle in a box, write an integral expression for the average value, or expectation value, of the momentum of the n=1 state
A particle in an infinite one-dimensional system was described by the wavefunction . Normalize this function. U= Ner2/21
for a particle in a one dimensional box of length L if the particle is on the n=4 state what is the probability of finding the particle within a) 0<x<5L/6 b) L/4<x<L/2 c) 5L/6<x<L