a) Solve the time-dependent Schrodinger equation for a particle of mass m in a ID infinite...

 

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a) Solve the time-dependent Schrodinger equation for a particle of mass m in a ID infinite box/well (i.e. V(x) = if a € [0, L] if a [0, L [6] ∞ b) Based on the extension of the previous question to two finite wells, explain how quantum tunneling and covalent bonding occur. [5] c) Show that the Hermite polynomials are solutions to the time-independent Schrodinger's equation for a particle of mass m confined to a quadratic well described by potential V(x) = mw²r². [6] d) Showing all the major steps for separation of variables, solve the time-dependent Schrodinger's equation for a Hydrogen atom and comment on the degeneracies in the gross structure solution. [8] a) Solve the time-dependent Schrodinger equation for a particle of mass m in a ID infinite box/well (i.e. V(x) = if a € [0, L] if a [0, L [6] ∞ b) Based on the extension of the previous question to two finite wells, explain how quantum tunneling and covalent bonding occur. [5] c) Show that the Hermite polynomials are solutions to the time-independent Schrodinger's equation for a particle of mass m confined to a quadratic well described by potential V(x) = mw²r². [6] d) Showing all the major steps for separation of variables, solve the time-dependent Schrodinger's equation for a Hydrogen atom and comment on the degeneracies in the gross structure solution. [8]

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