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EE606_s09_hw2

# EE606_s09_hw2 - Homework 2 Elements of Quantum Mechanics We...

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Homework 2 Elements of Quantum Mechanics 1. We used the relations and p E k ω = = ! ! in the expression 2 E mc = to derive Schrodinger equation for electrons. Repeat the same analysis for photons ( 0 0 m = ) to show that they obey classical wave-equation, i.e. 2 2 2 2 2 1 A A x c t = where A(x,t) is the amplitude of the wavefunction. 2. Theorists often approximate the potentials used in Schrodinger’s equation by simple analytical functions. For example, the potential of a molecule with two atoms can be approximated by V(x) = -V 0 δ (x-2a) - V 0 δ (x+2a). (a) Derive the derivative boundary condition for a delta function potential by integrating the Schrodinger equation across a delta function. (b) Compute the (implicit) expression for bound levels of the above molecule by writing the solution for x< -2a, -2a < x <2 a, and 2a < x and using the boundary conditions to connect the solutions. 3. Review the MATLAB script posted on the website to calculate first four energy levels of quantum well photo-detector as shown in the figure below.: (i) Submit the printout of the script you used.

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EE606_s09_hw2 - Homework 2 Elements of Quantum Mechanics We...

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