# Translational motion in Quantum Chemistry

1. Oct 5, 2007

### AbedeuS

Hello, I'm usually a PF user in General Physics/Chemistry, but I might need the help of you quantum physics users :), recently I have started a quantum chemistry module and I'd appreciate if I could clear some stuff up with you guys rather than look like a penis by asking all my friends, who probably dont understand as much as me either anyway.

Not quantum (but appeared in the quantum chem bit)

Now I've used the coulomb equation for about 3 years now, but It's always been slightly confusing for me, so just to clear it up:

$$V_{potential energy} = \frac{Q_{1}Q_{2}}{4\pi\epsilon_{o}r}$$

We have this (non-quantum) equation, sorry for ramming it in here, but I'd rather not spam by posting two threads, and this is probably basic for most of you guys, now for this equation. Lets say I have a proton and an electron, the maximum potential energy that they can have is "ZERO" (infinite seperation) and their lowest potential energy is negative "Infinity", so when an electron has potential energy of, say, -30eV, this would be equal to saying, if I gave the electron 30eV it would become infinitely seperated and have maximum potential energy?

Likewise for two alike charges (two positive) the maximum potential energy is Positive infinity and the lowest is Zero, so if I gave two Protons infinite energy they should be able to meld into eachover (lets not go into details, I'm just going to guess theres a limitation to how close they get before binding).

Translational Motion

Heres one that was pulled up in the lecture, translational motion was represented by a wavefunction, now I understand that Atoms will move in a "Wavelike" manner represented by the wavelength:

$$\lambda=\frac{h}{m}$$

but dont they have a particular position in space, mapping translational motion as a wavefunction would have massive implications for diffusion, gas velocity between two pressures and such, how does Quantum theory work around this?

Uncertanty theory

Now the lecturer just said uncertanty theory means we cant be sure about anything (which is true), If i could have a go at the explination around the uncertanty theory, if I wanted to localise the postion of a particle exhibiting a wavefunction, such as an electron, I would have to superimpose a sympathy of waves over it until the interference pattern divulged a particular position in the wavefunction where the proabability of it existing in the position is extremely high, but by this series of superpositions we cannot find out the momentum of the said wavefunction? Or is the equation:

$$m * p = \frac{h}{4\pi}$$

Where m and p are uncertanties of these quantities, i used an equals sign rather than an inequality sign because, i'm a newbie with Latex :)

Sorry for the hassle, but, your probably used to it so...*pokes your brain with a stick*

2. Oct 5, 2007

### AbedeuS

Anyone hooome? ^^

3. Oct 7, 2007

### AbedeuS

poke

4. Oct 23, 2007

### AbedeuS

pokey doke?

Im poking because its been inac for 3 weeks now ¬_¬ hehe

5. Oct 23, 2007

### Gokul43201

Staff Emeritus
This may be better suited to the homework/coursework forums.

Your understanding of the Coulomb potential is good. There is a deep misunderstand with what a wavefunction is, and your exposition on the HUP is also somewhat flawed.

Don't have time to address these now, but will check back later tonight.

6. Oct 23, 2007

### BerryBoy

OK right, you say negative infinity, but this is not the case. Protons and electrons cannot exist in the same place due to the pauli exclusion principle, this means that the closer you get them, there will eventually be an immense repulsive force, to stop you breaking the laws of physics; giving the electron POSITIVE energy when moved closer, so the graph for potential energy will probably look something more like this:

$$V = A^{12}/r^{12} - 2A^6/r^6$$ where $A$ is a constant that is the equilbrium distance for the orbit of the electron around a hydrogen nucleus (proton). Will probably make more sense if put into Mathmatica or Maple.

I'm tired can't answer the questions now, I'm sure someone else will :P

Sam :D

P.S. That equation was pulled out of a piece of coursework I had to hand in recently (I hope I remembered it right) :P