Find the reflection and transmission coefficients for particles incident from the left on a double potential barrier, with 0
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Q: Question: Particles with energy Ea.
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A: for cubical box,Lx=Ly=Lz=Land wave function ψ(x,y,z)=AsinnxπLxsinnyπLysinnzπLz
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- For the quantum harmonic oscillator in one dimension, calculate the second-order energy disturbance and the first-order eigen-state for the perturbative potentials: (in the picture)Given the same particle energy and barrier height and width, which would tunnel more readily: a proton, or an electron? Is your answer consistent with the usual rule of thumb governing when classical or non-classical behavior should prevail?Evaluate the E expressions for both the Classical (continuous, involves integration) and the Quantum (discrete, involves summation) models for the energy density u, (v).
- Solve the problem for a quantum mechanical particle trapped in a one dimensional box of length L. This means determining the complete, normalized wave functions and the possible energies. Please use the back of this sheet if you need more room.Plot the first three wavefunctions and the first three energies for the particle in a box of length L and infinite potential outside the box. Do these for n = 1, n = 2, and n = 3Find the ground-state energy and wave function of a system of N identical non-interacting particles confined in a one-dimensional infinity well when the particles are (a) bosons and (b) fermions with spin 1/2