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L7_1 - eigenfunctions and eigenvalues • The Hamiltonian...

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Wave Mechanics Erwin Schroedinger: an electron exhibiting wave-like properties can be described by a mathematical equation called wave equation. The electron is then described by a wave-function ( ψ ) corresponding to a standing wave, within the boundary conditions of the system under investigation. Ψ  e
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Schroedinger equation as an eigenvalue problem: first we introduce the concept of operators
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Schroedinger equation as an eigenvalue problem: eigenfunctions and eigenvalues a a
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Schroedinger equation as an eigenvalue problem:
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Unformatted text preview: eigenfunctions and eigenvalues • The Hamiltonian operator acts on the wavefunction and gives the energy of the particle • The wavefunction is an eigenfunction of the Hamiltonian operator and the energy is an eigenvalue of the Hamiltonian operator Schroedinger equation as an eigenvalue problem: eigenfunctions and eigenvalues Kinetic Energy Operator (1D) Momentum Operator (1D) • Is the function exp(ikx) an eigenfunction of the momentum operator?...
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