An electron is in a potential well that is 0.400 nm wide. (a) Find the ground-level energy of the electron E1-IDW, in eV, if the potential well is infinitely deep. (b) If the depth of the potential is only 0.015 eV, much less than E1-IDW, there is only one bound state. Find the energy, in eV, of this bound state.

(a) Consider the following wave function of Quantum harmonic oscillator: 3 4 V(x, t) = =Vo(x)e¯iEot +. Where, Eo, E, are the energy values corresponding to the ground state and the first excited state. Show that the expectation value of î in this state is periodic in time. What is the period? (b) Consider a quantum harmonic oscillator. The operator â4 is defined by : mw 1 â4 = 2h d: 2ħmw Find the expectation value of Hamiltonian for the state â4,(x). ma 1/4,- x2 and , (x) = - mw ma, x2 [Given ,(x) = () mw1/4 2mw x: 1. πή

An electron is in a finite square well that is 0.6 eV deep, and 2.1 nm wide. Calculate the value of the dimensionless potential (to 3 s.f).

An electron is trapped in an infinitely deep one-dimensional well of width 10 nm. Initially, the electron occupies the n = 4 state. Calculate the photon energy required to excite the electron in the ground state to the first excited state.