- Anharmonic Oscillator The Potential Energy V X Of A 10 Oscillator Of Mass M And Spring Constant K Is Given By 1 V X 1 (126.45 KiB) Viewed 19 times
- Anharmonic Oscillator The Potential Energy V X Of A 10 Oscillator Of Mass M And Spring Constant K Is Given By 1 V X 2 (28.55 KiB) Viewed 19 times
= Anharmonic Oscillator The potential energy V(x) of a 10 oscillator of mass m and spring constant k is given by: 1 V(x) = = kx2 + cx* ) 2 where c is a small constant compared to k such that the second term is small compared to the first term. a) Write down the eigenstate wavefunction of the ground state of a quantum harmonic oscillator as a function of x (see Chapter 2.3): Wo(x) = = = b) Treating H' = cx4 as a perturbation, show that to the first order, the effect of the perturbation is to change the ground state energy by E(1) = 36 (-), where w = 3c zmu k/m is the angular frequency.
c) Find the first order correction E(1) to the energy of the first excited state of the same quantum harmonic oscillator as above.