Question

2. The ladder operators can be used to determine the lowest eigenstate (ground state) of the harmonic oscillator by using the following relation of the annihilation operator, à alo) - 0 This equation is fundamental to ladder operators and implies that it is not possible to step down further in energy than the ground state. Determine the ground state wave function h(x (i.e. [0) using the relation above and the following information The annihilation operator is defined as: ) ·The moment urn operator is p--m You wl encounter a first order differential equation of the form: for which the general solution is ψ(r)-Cexp [-JA(r)dr]. Note that C is a normalisation constant, no need to calculate it! Solution: Simply using the relations gives: 2h here厔 (%)|w(z)-0 -V/mw what happens to this? Thus: gone (อ A(a)

Answer 1

It is simple mathematics step.

we had

sqrt (mw/2h) outside the brackets and the whole term on the left hand side is equal to zero.

Now, as per simple arithmetic we know that 0 divided by anything is zero.

so,

0 / sqrt (mw/2h) = 0 (after taking to the right hand side)

that's why you don't see sqrt (mw/2h) term in next step.