Read the summary and the most important questions on Quantum Mechanics

• 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 from vectors. Two vectors are orthogonal and if they are orthonormal they have the same unit length.  In some sense functions are vectors 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.

• 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 no timedependence. 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.