- #1

Aero

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1. Each observable has an associated Hermitian operator

2. States of systems are represented by complex functions on space-time

3. When an observable is to be measured, one can calculate the probability distribution by expanding the state of the system in eigenvectors of the observable's operator, and then the probability of measuring each eigenvalue is proportional to the component of the state vector in the eigenstate, squared.

Next, the operators themselves.

Is it correct that x^ = x

p^ = ih d/dx

t^ = t

E^ = ih d/dt ?

Schrodinger's equation: all that this says to me, in light of the above, is that

E^ = ((p^) ^ 2) / 2m + V

This seems perfectly reasonable on the one hand, because it suggests that familiar results about values of observables should be applied to operators of observables. However, on the other hand, it seems completely unreasonable to use a classical definition of energy in a quantum formulation.

One thing I do not understand at all, however, is the time-independent Schrodinger equation. What is its meaning, use or relevance?

Thanks

PS How can I use MathType to create LaTeX in this forum?