1. Consider the following normalized 1D wavefunction of a particle constrained to the interval x € (0, 1): -{V₁ y(x) = √630x²(x-1)², 0 < x < 1 (1) For the following parts you may express your answers where appropriate to two decimal places (rather than bothering to reduce ugly fractions). (a) What is the expected value of the position, (x), of this state? x<0 or x > 1

Physics Department PHYS4101 (Quantum Mechanics) Assignment 2 (Fall 2020) Name & ID#. A three-dimensional harmonic oscillator of mass m has the potential energy 1 1 1 V(x.y.2) = ; mw*x² +mwży² +=mw;z? where w1 = 2w a. Write its general eigenvalues and eigenfunctions b. Determine the eigenvalues and their degeneracies up to the 4th excited state c. The oscillator is initially equally likely found in the ground, first and second excited states and is also equally likely found among the states of the degenerate levels. Calculate the expectation values of the product xyz at time t

is this right?

4. Solve the "particle in a box" problem on the interval [0, 1] to determine the time-dependent wavefunction, 4(x, t), associated with the particle. At t= 0, the wavefunction is 4(x, 0) = 1 on the interval (0, n). What are the values of E, (these are the energy eigenvalues)? I will discuss this problem on Monday, and you may find Example 3 in section 13.3 helpful.