4.2 The potential energy in a MOFSET device near the
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
(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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