2. A particle is confined to the interval (-L/2. L/2) by infinite potentials for rs -L/2 and * 1/2 - Votol - ܘܐ V(x...
quantum mechanics
Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the doubly degenerate eigenstates are: Ιψη, p (x,y))-2sinnLx sinpry for 0 < x, y < L elsewhere and their eigenenergies are: n + p, n, p where n, p-1,2, 3,.... Calculate the energy of the first excited state up to the first order in perturbation theory due to the addition of: 2 2
Consider a particle confined in two-dimensional box with infinite...
A particle is confined to a one-dimensional box (an infinite well) on the x-axis between x = 0 and x L. The normalized wave function of the particle when in the ground state, is given by A. What is the probability of finding the particle between x Eo, andx,? A. 0.20 B. 0.26 C. 0.28 D. 0.22 E. 0.24
1. (50 points) Consider the particle in a one-dimensional box (0 s x S L). Assume a term is added to the Hamiltonian of the form: πχ V(x)g sin Sketch the potential and the expected eigenfunction (small g). In the limit of small g, find the second order correction to the ground state energy 2. (50 points) For a diatomic molecule rotating in free space, the Hamiltonian may be written: 12 21 Where L is the total angular momentum operator,...
3.9. A particle of mass m is confined in the potential well 0 0<x < L oo elsewhere (a) At time t 0, the wave function for the particle is the one given in Problem 3.3. Calculate the probability that a measurement of the energy yields the value En, one of the allowed energies for a particle in the box. What are the numerical values for the probabilities of obtaining the ground-state energy E1 and the first-excited-state energy E2? Note:...
A particle moves in 5 dimensional space (x, y, z, u, v). Its
Hamiltonian is given by
where the space is infinite in all directions except v which is
confined between v = 0 and v = a. Assume that the wave function
vanishes at v = 0 and v = a. Further,
= |E| 1 /~ 2 , where |E1| is the absolute value of the Hydrogen
ground state energy.
(d) What are the eigenstates of this Hamiltonian in...
1) Consider the 3 one-dimensional potentials below. 0 X-O For each of potentials, determine: a) Whether you expect parity symmetry to lead to a separation of even and odd eigenfunctions. Whether you expect the energy to be quantized, continuous, or both. b) Note: this is a math-free question
[1] Determine all potentials V(r0,) for which it is possible to find solutions of the time-independent Schroedinger equation which are also eigenfunctions of the operator L. (Help: The operator expression of the Hamiltonian for a particle of mass m in threedimensions is given (r))- 2m r ar2 1,2 2mr2
[1] Determine all potentials V(r0,) for which it is possible to find solutions of the time-independent Schroedinger equation which are also eigenfunctions of the operator L. (Help: The operator expression of...
1) Consider a particle with mass m confined to a one-dimensional infinite square well of length L. a) Using the time-independent Schrödinger equation, write down the wavefunction for the particle inside the well. b) Using the values of the wavefunction at the boundaries of the well, find the allowed values of the wavevector k. c) What are the allowed energy states En for the particle in this well? d) Normalize the wavefunction
1 Particle in a Box with a Bump (based on B&J 4.11) Consider a particle of mass m in a 1-D double well with potential given by Vo, 05\x\<b V(x) = { 0, b<\x<c 100, [x]>c . We will study the lowest energy states, for which 0 <E<V, corresponding to tunnelling between the two wells. (a) Write down the time-independent Schödinger equation in the three regions -c<x<-b, –b< <b, and b< I< c. Write down the most general wavefunction solution...
1/2) confined in a one-dimensional rigid box (an infinite Imagine an electron (spin square well). What are the degeneracies of its energy levels? Make a sketch of the lowest few levels, showing their occupancy for the lowest state of six electrons confined in the same box. Ignore the Coulomb repulsion among the electrons. (6 points) S =
1/2) confined in a one-dimensional rigid box (an infinite Imagine an electron (spin square well). What are the degeneracies of its energy levels?...