##

Introducing
and

The Hamiltonian for the **1D Harmonic Oscillator**

can be rewritten in terms of **the operator **

and its Hermitian conjugate

Both terms in the Harmonic Oscillator Hamiltonian are squares of operators.
Note that
is chosen so that
is close to the Hamiltonian.
First just compute the quantity

From this we can see that the **Hamiltonian can be written in terms of ** and some constants.

Jim Branson
2013-04-22