Summary: Quantum Mechanics
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MIT Quantum 2 - Lecture 1, 46:00 - 1:04:00 (1
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What are the two types of identities that play there own roles?
Eigenstates and orthonormality. -
What is the orthonormality in functions?
It is a concept fromvectors . Twovectors areorthogonal and if they areorthonormal they have the same unit length. In some sense functions arevectors in an infinite dimensional space. A vector but not in 3D dimensions.
If you have a function you have to give values of infinite many points and if you have a vector you have to give components. -
What is the more subtle properties?
A set of function is enough to expand any function. So any function can be written as a superposition. This refers to the property of completeness.
It is an assumption but it works! -
How can we still get a solution to the schrodingen equation?
This is THE solution to the schrodinger equation and not just a.
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What to do when you don't know the coefficient?
You can calculate them by using the orthonormality. You integrate it against another psy start -
How do we plug the integral back in?
You use a delta function because continuous variable -
So w have two things going on, how do we distinguish completeness and orthonormality?
Orthonormality - you sum over space and you keep labels
arbitrary - these functions depend on space on the labels
Completeness - you keep the positions
arbitrary but you keep the labels - you use a delta function
By looking at the mathematics you can see that there is a nice duality between them -
deel 1
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What is a stationary state?
When there is notimedependence . So whilst the wave function does depend on t. The probability density does not depend on it. -
What is an enegry eigenstate?
A solutiono to psix (TISE) associated with an energy E. -
How is the set of all alowerd values of E called?
The spectrum of the Hamiltonian.
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