# Quantum mechanics:Please and please answer ALL parts in a Correct and Neat manner.Please don't copy from

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**Question:**

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Electron with mass m* moves in a 1D quantum well with infinite barriers at x=0 and x=a. Assume mass of the electron to be m*=0.10 m where m is free electron mass. a. Write the Hamiltonian b. Obtain dimensionless Hamiltonian c. Solve stationary Schrodinger equation and obtain first, second and third energy levels d. write down explicitly NORMALIZED wavefunctions e. give energy levels (in meV) for a=10nm $1 92, 0, for the first three levels - plot them. f. determine expectation value of position <x> for the first two energy levels g. consider an electron in a state 7 +92) at t=0. Write explicitly the time evolution of this state in time.

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