It’s fair to ask “How much difference is there between a course in Quantum Chemistry and a course in Quantum Mechanics?” Simple answer: we don’t know. However, we postulate that Quantum Chemistry could be quite the same as Quantum Mechanics, just as Physical Chemistry I and Modern Physics I were quite the same.
Quantum Chemistry is a “Driver Subject” for our grade school education problem.
Postulates of Quantum Mechanics
Any system in a pure state can be described by a wave-function , ψ(t, x), where t is
a parameter representing the time and x represents the coordinates of the system. Such a function ψ(t, x) must be continuous, single-valued and square integrable.
- A function has to be continuous for us to calculate a first derivative. If our function is continuous over a domain of interest to us, then for every point c in that domain, the limit of f(x) as x approaches c is f(c).
To demand that the function be single-valued is a bit puzzling. A function has to be single-valued in order to be a function.
2. Any observable (i.e., any measurable property of the system) can be described by
an operator. The operator must be linear and hermitian.
Operators for Position and Momentum
The letter x is the variable for position and the letter p is the variable for momentum. In Quantum Mechanics, the operator for position is:
The operator for momentum is:
We might soon want to prove what is written below, but for now we’ll just show it:
The Commutator
Rob Sterling 