# Wave function

1. Dec 27, 2011

### wasi-uz-zaman

hi ,
can anyone please explain to me what is wavefunction - and can we apply schordinger wsve equation to simple pendulum.
thanks

2. Dec 27, 2011

### ibysaiyan

From my limited knowledge as of this moment, the way I think of wavefunction is basically a varying wave of numerous possibilities, it's upon observation which's when we break /collapse the wavefunction and make it definite.This is what happens in nature and how duality phenomena of light was discovered.

Schrodinger equation is a partial differential equation I am not sure whether there's a possibility of conversion from PDE to ODE. I will let other users give you a detailed explanation who are much knowledgeable on this.

3. Dec 27, 2011

### Markus Hanke

A wave function is a function that describes the probability amplitude of a system. In simple terms, it can be used to determine the probability of finding a system in a certain state at a certain time :

http://en.wikipedia.org/wiki/Wave_function

Yes, you can use it to describe a classic pendulum.

4. Dec 27, 2011

### eaglelake

Quantum mechanics only predicts the possible results of a measurement and the probability distribution of those results. We use the wavefunction$$\psi (x)$$
to calculate the probability distribution$$\left| {\psi (x)} \right|^2$$of the measurement results.$$\left| {\psi (x)} \right|^2$$gives us the probability of finding the particle at position$$x$$when we measure the position. It is a mathematical construct that is not an observable, i.e. we do not measure any of its attributes. Most believe that it is not a real physical entity; it does not propagate in space-time like real classical waves do. Mathematically it is defined as a vector in a Hilbert space, which is a complex linear vector space.

Schrodinger's time dependent equation $$i\hbar \partial \psi (x,t)/\partial t = \hat H\psi (x,t)$$can be applied to any quantum system, including the quantum simple pendulum. Usually, however, we only want to determine the energy levels and we solve instead the time independent Schrodinger equation$$\hat H\psi _k = E_k \psi _k$$, which is the energy eigenvalue equation.

Best wishes

5. Dec 29, 2011

### wasi-uz-zaman

thnaks a lot

6. Dec 29, 2011