Thermodynamics, Statistical Physics, and Quantum Mechanics

Note theform of thekineticenergy integralK,which again is obtained

from by an integration by parts. Again set the derivative of

equal to zero. This determines the value which minimizes the energy:

5.36 Halved Harmonic Oscillator (Stony Brook,

Chicago (b), Princeton (b))

a) Using the Rayleigh–Ritz variation principle, calculate the expec-

tation value ofthe groundstateenergy as afunction of

So our trialfunction is alreadynormalized.Continuingwith thenumerator
of (S.5.36.1), we have

First calculate the denominator of (S.5.36.1):

QUANTUM MECHANICS 283