Given a 3-dimensional particle-in-a-box system with infinite barriers and L-5nm, Ly-5nm and Li-6n...
Given a 3-dimensional particle-in-a-box system with infinite barriers and Lx=5nm, Ly=5nm and Lz=6nm. Calculate the energies of the ground state and first excited state. List all combinations of values for the quantum numbers nx, ny and nz that are associated with these states.
4. (20 points) Infinite Wells in Three Dimensions a) Consider a three dimensional in- finite rectangular well for which L -L, Ly-2L, ald L2-3L. In terms of quantum numbers (e.g. nz, ny, and n.), M. L, and ћ. write down an expression for the energies of all quantum states. (b) Find the energies of the ground state and the first three lowest lying energies. As in part (b), for each energy level, give the quantum numbers n, ny, n and...
Consider a quantum particle in a 3D box that is not a cube. It has side lengths: a = 1 Å b = 1 Å c = 2 Å Answer the following: 1. Derive the wave vector k in the terms of nx, ny, and nz 2. find the equation for energy as a function of nx, ny, and nz 3. List the five lowest energies a particle can have in this system and list all the different states for...
For a particle in a 3D box, with lengths L = Lx = 2 Ly = 14 Lz, provide a general expression for the energies in terms of L, and determine the quantum numbers associated with the lowest energy level that has a degeneracy of 3.
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...
Find parts a and b. Consider the three-dimensional cubic well V = {(0 if 0<x<a, 0<y<a, 0<z<a), (infinity otherwise). The stationary states are psi^(0) (x, Y, z) = (2/a)^(3/2)sin(npix/a)sin(npiy/a) sin(npiz/a), where nx, ny , and nz are integers. The corresponding allowed energies are E^0 = (((pi^2)(hbar^2))/2m(a^2))(nx^2+ny^2+nz^2). Now let us introduce perturbation V={(V0 if 0<x<(a/2), 0<y<(a/2)), (0 otherwise) a) Find the first-order correction to the ground state energy. b) Find the first-order correction to the first excited state. 1. Consider the...
An electron (mass m) is trapped ina 2-dimensional infinite square box of sides Lx - L - L. Take Eo = 92/8mL2. Consider the first four energy levels: the ground state and the first three excited states. 1) Calculate the ground-state energy in terms of Ep. (That is, the ground-state energy is what multiple of Eo? Eo Submit 2) In terms of Eo, what is the energy of the first excited state? (That is, the energy of the first excited...
4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny, and n, are integers. The corresponding allowed energies are Now let us introduce the perturbation otherwise a) Find the first-order correction to the ground state energy b) Find the first-order correction to the first excited state 4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny,...
Exercise 10.14 A particle is initially in its ground state in an infinite one-dimensional potential box with sides at x = 0 and x a. If the wall of the box at x-a is suddenly moved to x = 10a, calculate the probability of finding the particle in (a) the fourth excited (n = 5) state of the new box and (b) the ninth (n 10) excited state of the new box.
Particle with a speed bump Consider our old friend the 1D particle in the box, except now with a speed bump in the box so the potential now is given by L and L < x < L 0, Vo 0 x V (x) otherwise (a) Calculate the first order correction to the ground state (n = 1) and first excited state (n = 2) energies (b) Calculate the first order correction to the ground state wave function in terms...