A particle is in the n = 9 excited state of a quantum simple harmonic oscillator well. A photon with a frequency of 3.95 × 1015 Hz is emitted as the particle moves to the n = 7 excited state. What is the minimum photon frequency required for this particle to make a quantum jump from the ground state of this well to the n = 8 excited state? (Give your answer in Hz.)

A proton is in a one-dimensional box of width 7.8 pm (1 pm = 1 x 10-¹2 m). The energy of the proton is equal to the absolute value of the ground state of a hydrogen atom. What state is the proton in?

A Quantum system has a ground state with energy E0 = 100meV and a 3-fold degenerate excited state with energy E1 = 100meV . Calculate the probability of finding the system in its groud state when it is at T = 300 K?  a) 0.94 b) 0.06  c) 1  d) 0.98

A quantum simple harmonic oscillator consists of an electron bound by a restoring force proportional to its position relative to a certain equilibrium point. The proportionality constant is 8.11 N/m. What is the longest wavelength of light that can excite the oscillator? ps:- answer is not 443.68