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Question: 2 a state the time dependent schrodinger equation and its...

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2. (a) State the time dependent Schrodinger equation and its general solution. (1 mark) (b) Solve the time independent Schrodinger equation for an electron in a one dimensional infinite square well (-a<x<a), and hence derive an expression for how the position probability density of the electron varies in time given that: (i) the wave function is a superposition of the first two states of definite energy, and (ii) a measurement of the electrons energy is equally likely to result in either of these first two energies. State any assumptions you make, and explain clearly your reasoning at all stages. 6 marks) (c) Find an expression for the mean position of the electron described by this wave function, and describe how the mean position varies in time. What is the mean value of the electron energy? 3 marks) K-cos(2a) sin(ada 322 πχ Given dx=a where n is a non-zero integer .

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