Write down Pauli Spin matrix and find out (oo, -0,0). Also discuss the result.
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- Full explan pleaseresults. OAKL Consider a pne dimensional infinite-wall potential V = ∞ for > Land z<0, and V0 for There are two identical spin half fermions in this potential well and spin states are dened by) and 4) for spin up and down, respectively. a) (Very easy) Find the eigenvalues and the corresponding wave functions for the potential well. b) (Ensy) Write the full wave function for the fermions in singlet state with possible minimum energy. e) (Easy) Write the full wave function for the fermions in triplet state with possible minimum energyprovided a system of 2 electrons in a one-dimensional box, write the approximate wavefunctions including the spin (but without considering interelectronic repulsion) for the states with an electron with n=1 and an electron with n=2. State which of the resulting states has the lowest energy. Symbolically build the linear combinations of the wavefunctions products (including spin). SHOW FULL AND COMPLETE PROCEDURE IN A CLEAR AND ORDERED WAY
- Consider three noninteracting indistinguishable spin-0 particles trapped in a harmonic potential with energy states given as: [nx, Ny, nz). Consider three distinct single particle states: |0,0,0), |0,1,0), |0,2,0). Each of the particles can be in any one of the three states listed. How many different three particle states are possible?The operator în · ở measures spin in the direction of unit vector f = (nx, Ny, N₂) nx = sin cosp ny = sinesino nz = cose in spherical polar coordinates, and ở = (x, y, z) for Pauli spin matrices. (a) Determine the two eigenvalues of û.o.A system of 9 identical non-interacting spin-3/2 particles confined to a one-dimensional harmonic oscillator potential is in its minimum energy configuration for which E 5.75 eV. What is the minimum energy of the same system with 10 such particles? Recall that the energy levels of a single particle in a one-dimensional harmonic oscillator potential are given by En = (n+1) hwo with n = 0, 1, 2, .... =