operator?

[S.P.P]

I'm looking at this question:

'If we assume as oscillation of form y = Aexp(iwt) what is the operator w? What then is the operator for frequency f?'

I have no idea what is ment by operator. I've tried looking it up in books and the net, but the explinations im finding just aint helping me. Can anyone tell me how to find an answer to this question. (this isnt a homework question btw)


Another question (this is a homework question):

'An oscillation of frequency f dies out after approximately 10 seconds. What is the approximate spread of the frequencies.'

My question is, what is ment by spread?

[HallsofIvy]

What course are you taking and what are the problems around this one like?

I ask that because there can be a number of different answers to your question depending on the course.

In "basic" algebra, something like "y = Aexp(iwt)" would be a function of a real number and w would be a number. In linear algebra, t might be a vector in which case w would be a function taking one vector into another: an "operator". In quantum physics (not mathatics at all) what are numerical properties of of particles (position, velocity, momentum, energy, etc.) become operators on the quantum space. Certainly if you are expected to do a problem like this, you should already have been introduced to the notion of an "operator".

[S.P.P]

Its for a quantum mechanics course. The course started last week, and we've not covered much yet. I'm doing my own reserch into it. That problem was found on last years exam paper. Was just curious as to what an answer would be, and how u arrive at that answer.

[Tom Mattson]

The operator for ω is related to the operator for the energy E, since E=(hbar)ω (still haven't got this Latex thing down yet).

So, ω=(1/hbar)E=(1/hbar)(i*hbar)(∂/∂t)

or ω=i(∂/∂t). The operator for the frequency follows similarly from the relation between E and f, or from ω and f, whichever you like best.