Scrodinger Wave Equation

[aidan13791]

I know that this really isn't space science, but it seems the bestplace to ask, as a few of you probably have physics degrees; how do you do the equations from quantum physics, notably the Schrodinger Equation? I understand the theory perfectly, its just the maths, bearing in mind that I'm 15 and havent even done my GCSEs. <br /><br />Can anyone help?

 

[doubletruncation]

If you really want to learn how to do it, probably the best place to learn this is to find a good textbook. Personally, I like "Introduction to Quantum Mechanics", by David J. Griffiths (ISBN 0-13-124405-1) as a very good introductory text. The math involved is partial differential equations, and linear algebra - these are math subjects people usually learn after doing calculus. <br /><br />Bearing in mind that this is not going to be nearly as good an explanation as you would get from a textbook, I can maybe give you a flavor for how the math works. So there are more or less three different ways of doing the math for quantum mechanics: the Schrodinger way, the Heisenberg way, and the Feynman way. They have very different philosophies and strengths/weaknesses but you can show that mathematically they're all equivalent. In the schrodinger way, everything is encapsulated in the wavefunction. In the simplest case, consider just a single particle, and say we'd like to know where it's going to be at a given time t. In classical physics you might say you'd like to know the position as a function of time, x(t). In the Schrodinger method for quantum mechanics what you'd like to know is the wavefunction Psi(x,t) (it's some function of a space coordinate and time, meaning you give a value for t and a value for x then you get out a value for Psi. Psi can look like anything, the only constraint is that the area under the curve Psi*Psi_bar must be 1 (Psi_bar is the complex conjugate of Psi), or in other words the integral of the amplitude squared of Psi from minus infinity to +infinity must be 1). Psi has the following interpretation: Psi(x,t) * Psi(x,t)_bar *dx is the probability of finding the particle between x and (x+dx) at time t when you do an experiment to detect it (Note that after doing the experiment the wavefunction will be peaked at precisely where you found the particle). So if at time t=t0 the function Psi(x,t0) is very broad then the particle is really u <div class="Discussion_UserSignature"> </div>

 

[missmelo]

i want to know more information about it from you<br />

 

[aidan13791]

Ok, thanks very much for that, I kind of understand the maths now, not really enough to do it properly, but it isnt as confusing. I will get that book when I get some cash though.

 

[bobw]

<font color="yellow">Quantum mechanics is primarily used for studying the odd properties of atoms and the microscopic world.</font><br /><br />I really don't know anything about the Schrodinger Wave Equation and I'm not trolling for new team members but I thought you might be interested to know that the scientists over at Folding at Home have found a way to use it in thier distributed computing project.<br /><br />http://folding.stanford.edu/QMD.html<br /><br />"What is peculiar about QMD core? For other molecular dynamics simulation packages, interactions between atoms are described by an empirical potential energy (“force field approach”), which is an analytical function of atomic coordinates. In QMD core, there is no force field – atomic interaction is calculated using quantum chemical method or by solving Schrödinger equation." <div class="Discussion_UserSignature"> </div>

 

[alokmohan]

Can I sat acording this equation you may not know where a particle is lying at a certain rime.Do you mean that?