A symmetric infinite well has the potential energy (0 |x| < a V(x) = 100 |x| >a a. Write the corresponding Schrodinger equation and its solutions b. Write the boundary conditions c. Obtain the eigenfunctions and eigenvalues
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![1. A symmetric infinite well has the potential energy
V(x) = {
|x| < a
So
loo ]x| > a
a. Write the corresponding Schrodinger equation and its solutions
b. Write the boundary conditions
c. Obtain the eigenfunctions and eigenvalues](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c8ef47d-60df-4598-87ac-b0f98c8a9c79%2Fe90bd59d-03ff-4077-9981-553e3d0c0886%2Ff0wtqv5_processed.jpeg&w=3840&q=75)
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- 2 Consider a one-dimensional infinite well of width w along z-axis. Find the ground state energy and wave function of a system of N noninteracting identical particles that are confined to when the particles are bosons and spin 1/2 fermions.What is the answer of question 2Q5: Consider a particle of mass m in a two-dimensional box having side length L and L₁ with L = 2L, and V=0 in the box, ∞ outside; Suppose V=10 J in the box. What effect has this on the eigenvalues? the eigen functions?
- Let ynim denote the eigenfunctions of a Hamiltonian for a spherically symmetric potential (r). The expectation value of L, in the state +V5 w210+ V10 v1+ v20 w21 is 200Please don't provide handwritten solution ..... Determine the normalization constant for the wavefunction for a 3-dimensional box (3 separate infinite 1-dimensional wells) of lengths a (x direction), b (y direction), and c (z direction).The wavefunction for the motion of a particle on a ring is of the form ψ=NeimΦ . Evaluate the normalization constant, N. Show full and complete procedure in a clear way. DO NOT SKIP ANY STEP
- For the Osaillator problem, mwx2 har monit (부) (2M) y e Y, LX) = Mw 1. Use the lowering operator to find Yo(X). 2. Is your wave function normalized ? Check.Normalize the following wavefunction and solve for the coefficient A. Assume that the quantum particle is in free-space, meaning that it is free to move from x € [-, ∞]. Show all work. a. Assume: the particle is free to move from x € [-0, 00] b. Wavefunction: 4(x) = A/Bxe¬ßx²Let ynlm denote the eigenfunctions of a Hamiltonian for a spherically symmetric potential M7). The expectation value of L, in the state w+5 210 + v10 y-1 + /20 y 21, is %D
- O Consider the kinetic energy matrix elements between Hydrogen states (n' = 4, l', m'| |P|²| m -|n = 3, l, m), = for all the allowed l', m', l, m values. What kind of operator is the the kinetic energy (scalar or vector)? Use this to determine the following. For what choices of the four quantum numbers (l', m', l, m) can the matrix elements be nonzero (e.g. (l', m', l, m) (0, 0, 0, 0),...)? Which of these nonzero values can be related to each other (i.e. if you knew one of them, you could predict the other)? In this sense, how many independent nonzero matrix elements are there? (Note: there is no need to calculate any of these matrix elements.)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 = 3A particle of mass m is confined within a finite square well of depth V0 and width L.Sketch this potential, together with the form of the wavefunction and probability density for a particle in the lowest energy state. Briefly outline the procedure you would follow to determine the total number of energy eigenstates that can exist within a given finite square well.