# Mean number of oscilatory quanta?

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1. Jan 18, 2017

### upender singh

A quantum mechanical oscillator with the Hamiltonian
H1=p^2/2m +(m(w1)^2 x^2)/2

is initially prepared in its ground state (zero number of oscillatory quanta). Then the
Hamiltonian changes abruptly (almost instantly):
H1→H2=p^2/2m +(m(w2)^2 x^2)/2
What is the mean number of oscillatory quanta upon the transformation?

My first question is what does oscillatory quanta exactly means?

Attempt: Theory of quantum harmonic oscillator, the eigenstate formulas, the energy formulas. The only thing that is zero in ground state is n=0, so does it mean oscillatory quanta implies n quantum number.

2. Jan 18, 2017

### PeroK

You should have posted this in the homework forum, as you'll get a better response.

Let me explain the question at least. The oscillator is in a known state (ground state for first Hamiltonian). The Hamiltonian changes, which means that the energy eigenstates change. Now you have effectively an initial value problem. You know the initial state/wave function, and this you need to express as a linear combination of your new eigenstates.

I suspect the mean oscillatory quanta means the expected value of $n$ in your new system. Where $n$ represents the energy levels in your new system.

3. Jan 18, 2017

### upender singh

Hi Perok,
Sorry for posting it at wrong place.
Do you mean that the my initial state is the ground state of the old Hamiltonian. Now since the Hamiltonian has changed, I need to express it(ground state from old Hamiltonian) as a combination of the eigenstates of new Hamiltonian?

4. Jan 18, 2017

### PeroK

Yes, that's what you have here.