Wxe consider the harmonic oscillator in one-dimension write

Question

Wxe consider the harmonic oscillator in one-dimension
H = (-h/2m)(d²/dx²) + (1/2mω²x²)


1. Write down the lowest energy (ground state) wavefunction
2. Verify that the wavefunction is normalized.
3. Compute the expectation value of x, p, x² , p²
4. Compute the expectation value of the Hamiltonian.