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Quantum Mechanics (12.1-12.5)

Quantum Mechanics (12.1-12.5). Classical physics breaks down when one considers certain phenomena Electrons moving around a nucleus should decay into the nucleus Energy of blackbody radiators was proportional to frequency of light emitted, not intensity

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Quantum Mechanics (12.1-12.5)

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  1. Quantum Mechanics (12.1-12.5) • Classical physics breaks down when one considers certain phenomena • Electrons moving around a nucleus should decay into the nucleus • Energy of blackbody radiators was proportional to frequency of light emitted, not intensity • Energy in a blackbody is not continuous, but discrete (or quantized) • Light (a classical wave) sometimes behaves as a particle • Photoelectric effect is caused by light striking a metal surface and ejecting electrons • Energy of electron depends on frequency of light, not intensity • Electrons (classical particles) sometimes behave as waves • Electrons exhibit diffraction, just as light does • de Broglie hypothesized that particles have a wavelength

  2. Schrödinger’s Equation (13.1-13.3) • Schrödinger’s equation (SE) takes into consideration both the wave and particle nature of a classical particle (or system) • Classical wave equation can be mixed with de Broglie’s equation to give an overall equation for a particle’s (or system’s) energy • SE is a differential equation (DE) and its solution is called the wavefunction of the particle (or system) • All information about a particle (or system) is contained in the wavefunction • The energy of the system (and the form of the wavefunction) is primarily influenced by the potential energy of the system • Difficulty of solving the DE is also dependent on the form of the potential energy • SE is only exactly solvable for a few forms of the potential energy

  3. Properties of Wavefunctions (13.4-13.5) • The wavefunction itself has no physical meaning, but it is critical for understanding how a system behaves • Quantum mechanics deals in probabilities since the wavefunction has wave characteristics, thus a probability distribution function is required • Experimentally determined quantities (e.g., particle position) are influenced by probabilities, so their values are calculated through expectation values • Operators are used to represent some physical quantities (e.g., momentum) • Differential equations often have multiple solutions due to the nature of the boundary conditions • Solutions to the SE are orthogonal

  4. Photoelectric Effect

  5. Diffraction

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