1) a) A particle is in an infinite square well, with ground state energy E1. The wavefunction is3*y. Find in terms of E1. (There is an easy way to do this; no actual integrals4+5required.)b) A particle is in an infinite square well, with ground state energy Ej. Find a normalizedwavefunction that has a total energy expectation value equal to 3E1. (It will be asuperposition.) Keep all your coefficients real and positive.c) Now time-evolve your answer from part b, to show how the wavefunction varies withtime.

Answered: Image /qna-images/answer/c37bf10f-4341-44fe-95c5-6322c1d5b0e2.jpg

Answered: 1) a) A particle is in an infinite…

Similar questions

Given a Gaussian wave function: Y(x) = (1/a)-1/4e-ax²/2 Where a is a positive constant 1) Find the normalization (if the wave function is not normalized) 2) Determine the mean value of the position x of the particle : x 3) Determine the mean value of x? : x? 4) Determine the value of Ax = /(x²) – (x)²
Evaluate the E expressions for both the Classical (continuous, involves integration) and the Quantum (discrete, involves summation) models for the energy density u, (v).
The following Eigen function is a typical solution of the time-independent Schrödinger equation and satisfies boundary conditions for a particle in a confined space of a certain length. y(x) = sin (~77) (a) Plot the wave function as a function of x for L = 30 cm and n = 1, 2, 3 and 4. Note: You will need to have 4 plots in the same graph. (b) On a separate graph, plot the probability density (112) as a function of x using the conditions specified in part (a). Note: You will need to have 4 plots in the same graph. (c) Report your observations for parts (a) and (b)
4) Consider the one-dimensional wave function given below. (a) Draw a graph of the wave function for the region defined. (b) Determine the value of the normalization constant. (c) What is the probability of finding the particle between x = o and x = a? (d) Show that the wave function is a solution of the non-relativistic wave equation (Schrodinger equation) for a constant potential. (e) What is the energy of the wave function? (x) = A exp(-x/a) for x > o (x) = A exp(+x/a) for x < o
Question A2 Consider an infinite square well of width L, with V = 0 in the region -L/2 < x < L/2 and V → ∞ everywhere else. For this system: a) Write down and solve the time-independent Schrödinger equation for & inside the well, where -L/2< x
At time t = 0 the normalized wave function for a particle of mass m in the one-dimensional infinite well (see first image) is given by the function in the second image. Find ψ(x, t). What is the probability that a measurement of the energy at time t will yield the result ħ2π2/2mL2? Find <E> for the particle at time t. (Hint: <E> can be obtained by inspection, without an integral)