The energy of a molccule is the sum of the kinctic encrgics of the clec- trons and of the nuclei and of the various Coulomb energies. Suppose that for a particular many-particle norinalized wave function (x1,... ,XN), the expectation value of the kinetic encrgy is T and of the potential energy is -U(U > 0). (a) Find a variational estiinate of the ground state encrgy using a wave function X3N/2\x1,... , AxN) where A is a parameter. (b) Suppose y is the true ground state wave function and that the true ground state energy is -B(B > 0). What are the true values of T and U?
The energy of a molccule is the sum of the kinctic encrgics of the clec- trons and of the nuclei and of the various Coulomb energies. Suppose that for a particular many-particle norinalized wave function (x1,... ,XN), the expectation value of the kinetic encrgy is T and of the potential energy is -U(U > 0). (a) Find a variational estiinate of the ground state encrgy using a wave function X3N/2\x1,... , AxN) where A is a parameter. (b) Suppose y is the true ground state wave function and that the true ground state energy is -B(B > 0). What are the true values of T and U?
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Transcribed Image Text:The
energy
of a molccule is the sum of the kinctic encrgics of the clec-
trons and of the nuclei and of the various Coulomb energies. Suppose that
for a particular many-particle norimalized wave function (x1,... ,XN), the
expectation value of the kinetic encrgy is T and of the potential energy is
-U(U > 0).
(a) Find a variational estiinate of the ground state encrgy using a wave
function X3N/2 x1,... , AxN) where A is a parameter.
(b) Suppose y is the true ground state wave function and that the true
ground state energy is -B(B > 0). What are the true values of T and U?
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