Answer Happy

1a. Given y, and y, are stationary states of the same Hamiltonian with energies E, and E2 respectively. What is the condition on E, and E, such that the wavefunction ya +y, is also a stationary state? 1b. Same as in the above problem, suppose at 1 = 0 the particle has wavefunction ya +42. Write down (without doing any mathematics) its wavefunction at time t. You can assume that it is not in a stationary state so that your condition in the above question does not hold. 10. Sketch in the following diagram the probability density of a particle in an infinite square well potential when its quantum number is very largeſ, i.e., like a classical particle. ly 0 a 1d. Suppose y, is the lowest energy state of a quantum harmonic oscillator whose energy is E.. Explain in words (no mathematics) why a_y, must be a trivial solution, i.e., a_y. =0.