Think we are in a laboratory class room.
Think we are given a flask filled with hydrogen gas at room temperature and atmospheric pressure.
The hydrogen gas comprises N hydrogen atoms, i'th proton's space coordinate being denoted by Xi, and i'th electron by xi.
Which do you think right?
a. The gas is described by simple superposition of respective atomic hydrogen wave function.
That is, ENTIRE WAVE FUNCTION=PSY(X1,x1)timesPSY(X2,x2)timesPSY(X3,x3)....timesPSY(XN,xN)
That is, the states of each hydrogen atom are essentially independent with each other!
b. The gas is described by a intricate function that involves whole particle space variables simultaneously.
That is, ENTIRE WAVE FUNCTION=PSY(X1,X2,X3,..,XN,x1,x2,x3,...,xN, t) (t is time variable)
That is, the state of the whole gas is dependent on all of its constituent particle space variables and time variable.
How do you think?
Waiting your answers,
December 1, 2011
I would choose the latter. The wave function of the entire system depends on the positions of all the hydrogen molecules. If you were to simply sum up the inidividual wave functions you would essentially be ignoring the coulombic interactions between molecules.
Thank you for your response, Mr. Solomon.
This is an old aged student, not a professional, having learned physics about 35 years ago.
So my knowledge about gas physics is old.
As you indicated, a hydrogen gas comprises hydrogen molecules, each of which in turn comprises from two protons and two electrons. The two electrons are deemed to constitute a quantum mechanical cloud that is thought to shield the electric field of the nuclei almost completely. So that, when a molecule is flying freely, it does not in effect affect the states of the other molecules at all.
Is this correct?
After flying a mean free flight path, the hydrogen molecule will collide with another soon or later. Then, I think that a kind of completely elastic collision or another kind of interaction between the colliding molecules must occur. But exactly speaking, the detailed features of the collision must be difficult to be described by quantum mechanics, since the each case is vastly diverse. Since the shape of the hydrogen molecule can be imagined to be oblong oval or dumbell-shaped, the relative configuration between the two molecules at the instance of collision must be various. Further, three body collision may be also possibe.
Is this correct?
You spoke about Coulombic interaction between the molecules.
Is it attractive force or repulsive force, or both?
After collision, the state of the entire gas resumes its original state at least macroscopically, but not microscopically. As long as the total energy is kept constant, the seemingly effective functional form of the entire wave function does not change essentially.
Is this correct too?
The first question I proposed was what will be thought to represent the rough functional form for the wave fucntion of the entire hydrogen gas. Now, I have figured a rough picture of motions and collisions of the hydrogen molecules in the above sentences.
Are there some mistakes in the above discussion?
Do you have something to add?
Can we at least imagine or design the hypothetical functional form of the entire wave function of this hydrogen gas? Or do you prefer the statistical thermodynamic thinking?
How do you think?
Waiting your comments,
December 12, 2011