Basic treatment of the hydrogen atom through wave mechanics.

In summary, the book discusses the potential energy operator, the Schrodinger equation, and the use of spherical coordinates. The treatment of the hydrogen atom is archaic, and the use of units is archaic.
  • #1
scorpion990
86
0
Hey there. I'm trying to redo basic quantum chemistry with a lot more rigor. I'm currently using Pauling's "Introduction to Quantum Mechanics With Applications to Chemistry". Here is a copy of the page(s) I will be referring to:

http://books.google.com/books?id=vd...X&oi=book_result&resnum=5&ct=result#PPA113,M1

I'm getting caught up in the basic details. So... I have a few questions for the experts.

1. The potential energy operator is defined as -Ze^2/r. Excuse my stupidity, but why was the factor of k (1 / 4*pi*epsilon) left out? It seems like the rest of the equation is in SI.

2. The Schrodinger equation can be separated into the product of a wavefunction which deals with the translational motion of the atom, and another wavefunction which describes the interaction between the proton and electron... It makes sense to me to let x,y, and z equal the center of mass of the system. I'm a little confused as to why the "relative" x,y, and z coordinates are used for the substitution in spherical coordinates. Rather... I don't understand the consequences of such substitutions. You can't really interpret the system graphically in terms of the usual r/theta/phi, because they don't have their usual meaning in this case.

The rest is just calculus which I can definitely handle :) Any help would be appreciated.
 
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  • #2
I would pick up a more modern textbook, there are plenty of them
 
  • #3
scorpion990 said:
1. The potential energy operator is defined as -Ze^2/r. Excuse my stupidity, but why was the factor of k (1 / 4*pi*epsilon) left out? It seems like the rest of the equation is in SI.

He's probably using Gaussian (cgs) units, in which the unit of charge is defined such that Coulomb's Law reads

[tex]F = \frac{q_1 q_2}{r^2}[/tex]

http://en.wikipedia.org/wiki/Centimeter_gram_second_system_of_units
 
  • #4
Thanks to both =)

Why do you think I should pick up another book? Is the treatment of the hydrogen atom archaic, or is the use of units archaic? Every other undergraduate quantum chemistry book I looked at is really light on the math. And I don't quite feel the need to expose myself to too many applications which don't deal with chemistry.

Anyway... What book would you recommend?
 

1. What is the basic concept behind wave mechanics?

The basic concept behind wave mechanics is that particles, such as electrons, can also exhibit wave-like behavior. This means that instead of having a definite position and momentum, they have a probability of being in certain places at certain times.

2. How does wave mechanics explain the behavior of electrons in the hydrogen atom?

Wave mechanics uses a mathematical equation called the Schrödinger equation to describe the behavior of electrons in the hydrogen atom. This equation takes into account the wave-like nature of electrons and predicts their energy levels and positions in the atom.

3. What is the significance of the wave function in wave mechanics?

The wave function, denoted by Ψ, is a mathematical representation of the probability of finding an electron at a certain position in space. It is used to describe the behavior and properties of electrons in the hydrogen atom, and its square gives the probability density of the electron in a specific location.

4. How does wave mechanics differ from classical mechanics?

Classical mechanics describes the behavior of macroscopic objects, while wave mechanics is used to describe the behavior of subatomic particles, such as electrons. In classical mechanics, the position and momentum of a particle can be known with certainty, while in wave mechanics, these properties are described by probabilities.

5. What are the limitations of using wave mechanics to understand the hydrogen atom?

Wave mechanics is a mathematical model that is used to describe the behavior of electrons in the hydrogen atom, but it does not fully explain all of the physical properties of the atom. It does not take into account the effects of relativity or the magnetic properties of the electron, and it cannot fully explain the phenomenon of quantum tunneling.

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