Translational motion in Quantum Chemistry

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Homework Help Overview

The discussion revolves around concepts in quantum chemistry, particularly focusing on the Coulomb potential energy, translational motion represented by wavefunctions, and the uncertainty principle. The original poster seeks clarification on these topics, expressing confusion about their implications in quantum mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand the relationship between potential energy and separation of charges, questioning the implications of wavefunctions on translational motion and diffusion. They also explore the uncertainty principle and its effects on localization of particles.

Discussion Status

Some participants have provided feedback on the original poster's understanding, indicating that there are misconceptions regarding wavefunctions and the uncertainty principle. There is an acknowledgment of the need for further clarification, with one participant suggesting that the topic may be better suited for a different forum.

Contextual Notes

Participants note the complexity of the concepts being discussed, including the Pauli exclusion principle and the mathematical representation of potential energy, which may require additional context or information for a complete understanding.

AbedeuS
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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 don't 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. Let's say I have a proton and an electron, the maximum potential energy that they can have is "ZERO" (infinite separation) 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 separated 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 there's 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 don't 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 uncertainty theory means we can't be sure about anything (which is true), If i could have a go at the explanation around the uncertainty 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*
 
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poke
 
pokey doke?

Im poking because its been inac for 3 weeks now ¬_¬ hehe
 
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.
 
AbedeuS said:
Lets say I have a proton and an electron, the maximum potential energy that they can have is "ZERO" (infinite separation) 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 separated and have maximum potential energy?

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
 

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