determine whether the wavefunction for a particle in a 2d box eigenfunction (using Schrodinger equation)
determine whether the wavefunction for a particle in a 2d box eigenfunction (using Schrodinger equation)
prove that the particle in 2D box is an eigenfunction. vin वच 4R 2 m dy 2 2 m 2x function of (
For each pair, determine if the wavefunction is an eigenfunction of the operator listed. If the wavefunction is an eigenfunction of the operator, clearly identify the corresponding eigenvalue. (a) = + + = Aerky a pika w piks z (b) 3 = tan(ka) 4 = sin(km) Note: tan(x) = 3
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is represented by the wavefunction v(x) 0, otherwise a. Sketch the wavefunction. Write down the (time independent) Schrodinger equation. Show whether or not the wavefunction is a solution to the equation. b. What does it mean physically if the wavefunction of the particle is NOT a solution to the Schrodinger equation? Explain. c. Determine the normalization constant A. 5. Same system. Find the average or...
10 points Save Answer In solving Schrodinger equation for a particle in a box problem, what is the major condition that forces the energy level to be discrete? TT T Arial 3 (12pt) ΑΕς • T
Consider a particle of mass m inside a 2D box of sides a. Inside the box, the potential is zero and the outside is infinity (a) Show that overall wavefunction is given by y(x,y)= / Sin! Sin | where nį, n2 = 0,1,2,... 14 in x 1 anv (b) Find an expression for the density of states.
09 Estimate the ground state energy and wavefunction for a particle in a box using the variational method with the following trial wavefunction, where N is the normalization constant and ß is a variational parameter that should be minimized. 14) = N exp(-Bx2) (7.6) 1. Is this a good trial wavefunction for this approximation (justify your answer)? 2. Why is this not a good wavefunction? 3. Can you solve this problem both analytically and numerically? Pay careful attention to limits...
Wavefunction given is Psi (2,2) for a 2D particle in a square (both sides of the square have the same length a). Write down the most probable location(s) for the particle, give coordinate(s)
5 Suppose that a particle in a 1-dimensional box is in the state (x) = NxL-x) OSxSL = 0 everywhere else a) Show that this wavefunction is not an eigenvalue of the Hamiltonian operator. b) Sketch the wavefunction (x) c) Determine the value of the normalization constant N ! What this means is that the state is not stationary. so it evolves in time according to the full time-dependent Schrodinger equation. The expression given for (x) represents one instant in...
A particle in a 1D box is described by the following normalized wavefunction: 40(x) = (*)"'* sin() Determine the probability that the particle will be found in the region 3
8. Consider one electron in a 1D box of side L. Its wavefunction is given by V3 V3 2V3i where ф1(x), фг(x), and фз(x) are the first 3 eigenfunctions of the Hamiltonian, A, of a particle in a 1D box, h2 d2 a) Is Ψ(x) normalized? If it is not normalized it, normalize it! b) Is ų (x) an eigenfunction of A? If it is an eigenfunction, what is the eigenvalue?