Can Someone Explain the Wave Function?

[Achrelos]

I am having some trouble understanding the wave function. I tried to look up the formula to maybe understand what was going on with the orbitals. I found the formulas, but I have no idea what I am looking at. There are certain variables I understand, and certain ones I do not. I was hoping someone here could explain the basics of the wave functions to me.

[Mike Smith Cosmos]

Here is the Wikipedia link the first few paragraphs have a simple ISH explanation.


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

Hope this is a start.

Mainly to do with where a particle ,like an electron is likely to be in orbit. Namely orbitals.

Mike

Ps Schreoniger produced this formulae With svie (Greek letter ) The thing that looks like the devils fork.

Non mathematicians usually feint at this point and run screaming into the nearest lake. Do not dispare a hand will appear out of the sky to take you to safety.

 

If you look to the sun rising high to the east, you will see a dark shadow move across the face of the sun,, in the shape of a swan. Fear not, go with the swan, he will not harm you.. but Luke beware, do not go across to the dark side.

Edited November 13, 2013 by Mike Smith Cosmos

[Sensei]

Ps Schreoniger produced this formulae With svie (Greek letter ) The thing that looks like the devils fork.

 

 

Psi

http://en.wikipedia.org/wiki/Psi_%28letter%29

[Pixel]

Which variables do you not understand?

Edited January 24, 2014 by Pixel

[Mike Smith Cosmos]

I give up !

 

I can not get the link organised to Erwin Schrödinger , or however the name is ...xxx. spelled !

 

I am trying to work on my I pad and the thing has a mind of its own . My fingers are too fat , my eyes are too unfocused, my brain is too slow , and I need a drink !

 

 

One spin-0 particle in one spatial dimension[edit]

 

Standing waves for a particle in a box, examples of stationary states.

 

Travelling waves of a free particle.

The real parts of position and momentum wave functions Ψ(x) and Φ(p), and corresponding probability densities |Ψ(x)|2 and |Φ(p)|2, for one spin-0 particle in one x or p dimension. The wavefunctions shown are continuous, finite, single-valued and normalized. The colour opacity (%) of the particles corresponds to the probability density (not the wavefunction) of finding the particle at position x or momentum p.

For now, consider the simple case of a single particle, without spin, in one spatial dimension. (More general cases are discussed below).

Position-space wavefunction[edit]

The state of such a particle is completely described by its wave function:

,

where x is position and t is time. This function is complex-valued, meaning that Ψ(x, t) is a complex number.

Interpreted as a probability amplitude, if the particle's position is measured, its location is not deterministic, but is described by a probability distribution. The probability that its position x will be in the interval [a, b] (meaning a ≤ x ≤ b) is:

 

where t is the time at which the particle was measured. In other words, |Ψ(x, t)|2 is the probability density that the particle is at x, rather than some other location; see probability amplitude for details. This leads to the normalization condition:

 

because if the particle is measured, there is 100% probability that it will be somewhere.

 

 

 

 

This is how the equation works out in practice from the Schrödinger equation , for hydrogen atoms

 

 

 

 

Mike ( no this is Schrödinger )

Edited January 24, 2014 by Mike Smith Cosmos

[MigL]

The use of a suitable operator with the wave function will provide a probability distribution of the observable ( energy levels, momentum, spin, position, etc. ) related to said operator.

 

See the previously posted electron orbital probability distributions.

Edited January 24, 2014 by MigL

[Achrelos]

Sorry everyone, I got taken up with finals way back when and totally forgot about this forum. I know it's very late, but thanks for the replies and I will attempt to not abandon the place again.

[Enthalpy]

Wave functions don't require much imagination any more because now you see them:

http://physicsworld.com/cws/article/news/2009/aug/27/molecules-revealed-in-all-their-glory-by-microscope

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.94.026803 (click two last ipctures)

http://io9.com/the-very-first-image-of-a-hydrogen-bond-1426759827

 

One funny idea about the atomic force microscope, as opposed to the scanning tunnel microscope, is that you observe the same electron pair all the time. This is not a statistic over many successive electrons. It helps to understand whether an interaction between two particles needs to reduce them to points or not, and more interesting thoughts.

[Deepak Kapur]

i think the schodinger wave equation is for a configuration of particles rather than a single particle....

[Nicholas Kang]

Yes, I think so. Schrodinger`s Wave Equation must obey Heisenberg`s Uncertainty Principle.

[ajb]

i think the schodinger wave equation is for a configuration of particles rather than a single particle....

 

 

It is okay for single particles and is usually how it is introduced. Otherwise it becomes much more complicated than it needs to be at first look.

Yes, I think so. Schrodinger`s Wave Equation must obey Heisenberg`s Uncertainty Principle.

 

 

The equation itself does not satisfy the uncertianty principle, the solutions give you the standard deviations of the observables, which gives you the UP.

Edited June 30, 2014 by ajb

[Nicholas Kang]

You mean UP is derived from SWE?

[studiot]

Nicholas, you are obviously keen but have not yet met many of the deeper points and connections of mathematics.

These are not introduced in courses taught at your school level and, I'm sorry to say, that some of the groundwork that used to be taught is missing today.

So you will have to seek out some of this for yourself.

That can be an exciting journey for those who are interested in such matters!

 

 

You need to fully understand the difference between an equality and an identity. They are different, although we usually use the equals sign for both.

 

Similarly you need to fully understand what is meant by the statement; "X satisfies this equation or that condition".

Also important is what mean when we say 'solve an equation'.

In elementary mathematics, particularly applied maths or physics etc, this often means

"plug in the known quantities and find the unknown quantity"

Otherwise called 'plug and chug'

 

 

Schrodinger's equation is an example of a type of equation that has an infinite number of solutions.

But we do not use Schrodinger's equation in isolation, a proper description also comes with some (a set of) 'boundary conditions'.

These boundary conditions are additional mathematical statements, which may be equations to solve in their own right, which allow us to pick out a solution from all the infinite possibilities, appropriate to the system in hand.

 

This combination of a key equation, statement, principle, law, or theorem with other information is very common to the point of being the norm.

 

Having worked through all this we extract from the Schrodinger equation, along with the problem boundary conditions, a function or functions functions.

Somtimes this function is such that it obeys an uncertainty principle.

 

Note this idea of uncertainty applies to many equations,even simple algebraic ones.

 

For example the equation

 

3x²+8x+6 = (x²+4x+1) +(2x²+4x+5)

 

is infinitely uncertain since it is true (satisfied) for any or all values of x.

(Note this is actually an example of an identity that I mentioned earlier)

 

Whereas the equation

 

3x²+8x+6 = 2x²+5x+4

 

is precise (certain) since it is only true for two specific values of x, namely x= -1 and x=-2.

(note this is an example of an equality).

Edited June 30, 2014 by studiot