Solve the schordingers equation for a particle in a rigid two-dimensional box.

Expert Solution

Plz note this is my work not a copied one ...plz rate if that helps

genius_generous answered 2 years ago

5. Consider a particle in a two-dimensional, rigid, square box with side a. (a) Find the...

5. Consider a particle in a two-dimensional, rigid, square box with side a. (a) Find the time independent wave function φ(x,y)describing an arbitrary energy eigenstate. (b)What are the energy eigenvalues and the quantum numbers for the three lowest eigenstates? Draw the energy level diagram

For two dimensional particle in a box, how many electrons can we get at most in...

For two dimensional particle in a box, how many electrons can we get at most in the first energy level and why?

Use the one-dimensional particle-in-a-box model with impenetrable walls and the equation R = R_0*A^(1/3) to estimate...

Use the one-dimensional particle-in-a-box model with impenetrable walls and the equation R = R_0*A^(1/3) to estimate the minimum kinetic energy of a nucleon in a nucleus. Express your answer in MeV and in terms of a number 'n' the mass number 'A', and an exponent p, which is the ratio of two integers, resulting in K = n/A^p.

Consider a particle of mass m confined to a one-dimensional box of length L and in...

Consider a particle of mass m confined to a one-dimensional box of length L and in a state with normalized wavefunction. For a partide in a box the energy is given by En = n2h2/8mL2 and, because the potential energy is zero, all of this energy is kinetic. Use this observation and, without evaluating any integrals, explain why < px2>= n2h2/4L2

Use the quantum particle wavefunctions for the kinetic energy levels in a one dimensional box to...

Use the quantum particle wavefunctions for the kinetic energy levels in a one dimensional box to qualitatively demonstrate that the classical probability distribution (any value of x is equally allowed) is obtained for particles at high temperatures.

Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal....

Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal. Namely, find the relation between m and n so that < m | n > = 0

Write a function to solve the two-dimensional in Matlab, unsteady heat conduction equation with no internal...

Write a function to solve the two-dimensional in Matlab, unsteady heat conduction equation with no internal heat generation on a square domain. The length of each side of the square is 1 m. The function will have the following 4 inputs: npts number of grid points in each coordinate direction nt number of time steps to take dt size of time step (s) alpha thermal diffusivity (m2/s) Use the following initial and boundary conditions: Initialize the body to T =...

Solve the two-dimensional wave equation in polar coordinates and discuss the eigen values of the problem.

Consider a particle of mass m that can move in a one-dimensional box of size L...

Consider a particle of mass m that can move in a one-dimensional box of size L with the edges of the box at x=0 and x = L. The potential is zero inside the box and infinite outside. You may need the following integrals: ∫ 0 1 d y sin ⁡ ( n π y ) 2 = 1 / 2 , for all integer n ∫ 0 1 d y sin ⁡ ( n π y ) 2 y = 1...

For a particle of mass m in a two-dimensional potential well(i.e. particle confined in a 2D...

For a particle of mass m in a two-dimensional potential well(i.e. particle confined in a 2D box) with sides L1 and L2: a) Set up the Schrödinger equation for this system. b) Using separation of variables, derive an expression for thewavefunction Ψ and for the energy levels of the system. Be sure toshow all of your work for this derivation. c) For the case of square potential well with side L (i.e.L1=L2=L), sketch an energy level diagram forthe nine lowest...

Question