a) Derive the following commutator relationships between the components of angular momentum L and of p: (i) [Ly, px] = −ih(bar)pz (ii) [Ly, pz] = ih(bar)px (iii) [Ly, p2x ] = −2ih(bar)pxpz (iiii) [Ly, p2z ] = 2ih(bar)pxpz (b) Hence show that the square L2 of the angular momentum operator L commutes with the kinetic energy operator p2/2m = (p2x + p2y + p2z )/2m.
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.
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.
The top view of a table, with weight Wt, is shown in the figure. (Figure 1) The table has lost the leg at (Lx, Ly), in the upper right corner of the diagram, and is in danger of tipping over. Company is about to arrive, so the host tries to stabilize the table by placing a heavy vase (represented by the green circle) of weight Wv at ( X, Y). Denote the magnitudes of the upward forces on the table...
ly lx Switch lx2 2) Closing the Loop We have the circuit shown above, where the segment lengths are defined as: lx-4 cm, lx2 1 cm; Iy-2 cm, ; 1 0.32 Tesla. If the switch is opened at t=0, graph the change in voltage as a function of time. Explain why your solution is accurate, and what is physically happening in the circuit. ly lx Switch lx2 2) Closing the Loop We have the circuit shown above, where the segment...
Analyze a quantum wire with a rectangular cross-section of dimensions Lx=Ly. Assume infinite potential well. Looking for the three lowest confinement energies.
3. (18 points) The angular momentum operator in the y direction is given by: ly- while the position operator in the x direction is given by: & x. a. (10 points) Determine the commutator for these operators when applied to the dummy function f(x). b. (8 points) What does the value of the commutator tell us about the relationship between the quantum mechanical observables associated with these two operators? Explain 3. (18 points) The angular momentum operator in the y...
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.
A cubical box of widths Lx-Ly-24.0 nm contains eight electrons. What is the energy of the ground stat system? Assume that the electrons do not interact with one another, and do not neglect spin. 123 eV ▼ the tolerance is +/-2% Click if you would like to Show Work for this question: Open Show Wo rk
2, Explicitly construct the three 3 × 3 matrices that represent (a) Lx, Ly, and Lz in the space of 1 1 functions: (Li/m , m' s(1-1, ml Lill = 1,m') 1m where i = x, y, z. (b) Show by explicit calculation that these three matrices obey the commutation relations of angular momentum (c) Find the matrices that represent L.+, L, and L2