WarmUp Exercise #16, 10/18  (Assignment Due 10/23)

Please answer the  following 3 questions regarding the operator we call a-hat.

The operator we call a-hat is defined as a-hat = (2m hbar w) ^-0.5 ( ip + mwx ), where x and p are our usual position and momentum operators.

Questions

1.  What is the unit of a-hat?

2.  What is a-hat ^dagger (the adjoint of a-hat)? Is it Hermitian?

3. What combination of a-hat, a-hat ^dagger, and suitable constants looks like the harmonic oscillator Hamiltonian? How close can you get it?

Answer in the form below, a short answer for each is fine. 
This report is due by 8:00 am Tuesday morning.