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  1. Sep 2022
  2. chem.libretexts.org chem.libretexts.org
    3.7: The Average Momentum of a Particle in a Box is Zero
    1
    1. sarahconnollychapman 15 Sep 2022
      orthogonality is thought of as describing non-overlapping, uncorrelated, or independent objects of some kind

      see equation below for how to define two functions as being orthogonal

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    chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/03:_The_Schrodinger_Equation_and_a_Particle_in_a_Box/3.07:_The_Average_Momentum_of_a_Particle_in_a_Box_is_Zero
  3. chem.libretexts.org chem.libretexts.org
    4.1: The Wavefunction Specifies the State of a System
    2
    1. sarahconnollychapman 15 Sep 2022
      single valued, continuous, and finite.

      these are the requirements of a wavefunction

    2. sarahconnollychapman 15 Sep 2022
      The state of the system is completely specified by ψψ\psi. All possible information about the system can be found in the wavefunction ψψ\psi.

      first postulate of quantum mechanics: all the info we need about a system can be figured out using the wavefunction

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    chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/04:_Postulates_and_Principles_of_Quantum_Mechanics/4.01:_The_Wavefunction_Specifies_the_State_of_a_System
  4. chem.libretexts.org chem.libretexts.org
    4.5: Eigenfunctions of Operators are Orthogonal
    1
    1. sarahconnollychapman 15 Sep 2022
      orthogonal

      orthogonal=events are statistically independent of one another

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    chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/04:_Postulates_and_Principles_of_Quantum_Mechanics/4.05:_Eigenfunctions_of_Operators_are_Orthogonal