# Schrodinger wave equation

1. May 4, 2004

### Stranger

according to quantum mechanics there are many possiblities for a anything to happen....for example if there is a soap on the table..it exists only when we see it....only when we 'actualize' the wave-function....but what about the characteristic smell of the soap doesnt that make it exist? Does the schrodinger equation incorporate this??

2. May 4, 2004

### ZapperZ

Staff Emeritus
You need to be aware that in QM, when you make A measurement, you are obtaining a particular PROPERTY of the system. The wavefunction, which is the solution of the Schrodinger equation, contains the information of ALL the observable properties of the system. When you observe the soap, you are making a measurement of it's POSITION. This is just ONE possible properties that is contained in the wavefuction.

Now, what happen to the other properties or observables AFTER you make such measurement. This is where you really have to study and understand QM to appreciate what it is trying to convey. An observable is represented by what is known as an operator in QM. But what is interesting here is that various different operators have this property where they need not commute with each other. Let me explain...

Commutation relations in algebra says that AB is the same as BA. If A and B do not commute, it means that AB-BA is not zero. Then the ORDER that you multiply these two things matter!

In QM, if two operators commute (i.e. AB-BA=0), then if you make a measurement of the property of A, you automatically know the property of B (if the system is non-degenerate). However, if two operatores do not commute, then if you measure the observable represented by A, then the values of B are still indetermined. One has not "collapsed" (I hate that word) all the superposition of the various values of B by measuring the property A.

So, if you can figure out how the "Smell" operator relate to the position operator of the soap, then I can tell you what you will get as far as QM is concerned.

Zz.

Last edited: May 4, 2004