(a) Using A 0 from Problem 6-34, write down the total wave function 0 (x, t) for the ground state of a harmonic oscillator.

(a) Using A₀ from Problem 6-34, write down the total wave function Ψ₀(x, t) for the ground state of a harmonic oscillator.

(b) Use the operator for p_x from Table 6-1 to compute (p²).

Problem 6-34

Compute (x) and (x²) for the ground state of a harmonic oscillator (Equation 6-58). Use A₀ = (mω/ћπ)^1/4.

Symbol Physical quantity Px Py P E E Ex Table 6-1 Some quantum-mechanical operators L Any function of x-the position x the potential energy V(x), etc. x component of momentum y component of momentum z component of momentum Hamiltonian (time independent) Hamiltonian (time dependent) Kinetic energy z component of angular momentum Operator f(x) d i x a 2m i ay d 2 Pop i az + V(x) ih- at 2 2m ax -ih