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1: The Basic Tools of Quantum Mechanics

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    60508
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    Quantum Mechanics Describes Matter in Terms of Wavefunctions and Energy Levels and physical Measurements are Described in Terms of Operators Acting on Wavefunctions

    • 1.1: Operators
      Each physically measurable quantity has a corresponding operator. The eigenvalues of the operator tell the values of the corresponding physical property that can be observed
    • 1.2: Wavefunctions
      The eigenfunctions of a quantum mechanical operator depend on the coordinates upon which the operator acts; these functions are called wavefunctions
    • 1.3: The Schrödinger Equation
      The Schrödinger Equation is an eigenvalue equation for the energy or Hamiltonian operator; its eigenvalues provide the energy levels of the system.
    • 1.4: Free-Particle Motion in Two Dimensions
      The number of dimensions depends on the number of particles and the number of spatial (and other) dimensions needed to characterize the position and motion of each particle
    • 1.5: Particles in Boxes
      The particle-in-a-box problem provides an important model for several relevant chemical situations
    • 1.6: One Electron Moving About a Nucleus
      The Hydrogenic atom problem forms the basis of much of our thinking about atomic structure. To solve the corresponding Schrödinger equation requires separation of the r, θ, and ϕ variables  The Hydrogenic atom problem forms the basis of much of our thinking about atomic structure. To solve the corresponding Schrödinger equation requires separation of the r, θ, and ϕ variables .
    • 1.7: Harmonic Vibrational Motion
      This Schrödinger equation forms the basis for our thinking about bond stretching and angle bending vibrations as well as collective phonon motions in solids
    • 1.8: Rotational Motion for a Rigid Diatomic Molecule
      This Schrödinger equation relates to the rotation of diatomic and linear polyatomic molecules. It also arises when treating the angular motions of electrons in any spherically symmetric potential
    • 1.9: The Physical Relevance of Wavefunctions, Operators and Eigenvalues
      Quantum mechanics has a set of 'rules' that link operators, wavefunctions, and eigenvalues to physically measurable properties. These rules have been formulated not in some arbitrary manner nor by derivation from some higher subject. Rather, the rules were designed to allow quantum mechanics to mimic the experimentally observed facts as revealed in mother nature's data. The extent to which these rules seem difficult to understand usually reflects the presence of experimental observations.


    This page titled 1: The Basic Tools of Quantum Mechanics is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jack Simons via source content that was edited to the style and standards of the LibreTexts platform.

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