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.
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...
3) List the first 6 states in a 3 dimensional box where Lx=L, Ly=2L, and L=4L. For each energy level write its degeneracy.
Given a 3-dimensional particle-in-a-box system with infinite barriers and L-5nm, Ly-5nm and Li-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. Given a 3-dimensional particle-in-a-box system with infinite barriers and L-5nm, Ly-5nm and Li-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...
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
Consider a perturbed particle in a box, with potential energy: for x <-L/2 2brx/L for -1/2sxSL2 for x >L/2 nd confining the zero order functions to n-1,2, 3, 4 (i.e. the lowest four Using Matrix algebra, and confining the zero order functions to n solutions to the unperturbed particle in a box problem) determine the energy of the l (Hint: In diagonalizing a matrix, you may reorder the quantum numbers in any way you like). d) Consider a perturbed particle...
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...
The energy levels for a particle in a 1-D box of dimension (L) is provided by the following expression: n h2 E, 2mL2 where m is the mass of the particle, h-bar = h/2 andn is the quantum number. Evaluate the energy associated with the first level (n 1) for an argon atom in a 10 A 1-D box. Select one: a. 8.27 x 10-25 kJ/mol b. 4.98 x 10 1 kJ/mol c. 8.27 x 1028 kJ/mol d. 4.98 x...
8. A particle in a box (0x<L) has wave functions and energies of En 8m2 a) Normalize the wave functions to determine A b) At t-0, ψ(x)-vsv, + ψ2 . 2. c) The particle will oscillate back and forth. Derive an expression for the oscilla- tion frequency in terms of h, m, and L Derive expressions for Ψ(x, t) and |Ψ(x, t)
Determine for an electron in a 2 Dimensional box two pairs of quantum numbers which will cause degenerate energy given the following parameters: Lx= 2nm Ly = 3nm