4.2 The potential energy in a MOFSET device near the metal oxide ...

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4.2 The potential energy in a MOFSET device near the metal oxide interface is approximately V(x) laex 00 for x <0 = for x > 0 where a is the electron charge, and E is the electric field strength. Use the variational technique to estimate the ground state energy of an electron in this configuration. (Hints: a) use the un-normalized trial function 0 (x) = x exp (-ax2) ). b) Find the normalized trial wave-function. c) Compute the energy functional (i.e. the expectation value of the Hamiltonian for the state of the system assumed given by the trial function). d) Find the value of a at the extremum of the energy functional. e) Compute the approximate ground state energy). 4.3 Repeat the same steps as in Pb. 4.2 for the normalized Schrodinger equation = - dx2

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