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1: Overview of Time-Independent Quantum Mechanics

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    • 1.1: Describing a System Quantum Mechanically
      As a starting point it is useful to review the postulates of quantum mechanics, and use this as an opportunity to elaborate on some definitions and properties of quantum systems.
    • 1.2: Matrix Mechanics
      Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics.
    • 1.3: Basic Quantum Mechanical Models
      This section summarizes the results that emerge for common models for quantum mechanical objects. These form the starting point for describing the motion of electrons and the translational, rotational, and vibrational motions for molecules. Thus they are the basis for developing intuition about more complex problems.
    • 1.4: Exponential Operators
      Throughout our work, we will make use of exponential operators that act on a wavefunction to move it in time and space. Therefore they also referred to as propagators. Of particular interest to us is the time-evolution operator.
    • 1.5: Numerically Solving the Schrödinger Equation
      Often the bound potentials that we encounter are complex, and the time-independent Schrödinger equation will need to be evaluated numerically. There are two common numerical methods for solving for the eigenvalues and eigenfunctions of a potential. Both methods require truncating and discretizing a region of space that is normally spanned by an infinite dimensional Hilbert space.

    1: Overview of Time-Independent Quantum Mechanics is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Andrei Tokmakoff via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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