phys documents (dragged) 51

phys documents (dragged) 51 - k, t ) = 1 h ( x, t )e-ikx dx...

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Chapter 10 Quantum physics 10.1 Introduction to quantum physics 10.1.1 Black body radiation Planck’s law for the energy distribution for the radiation of a black body is: w ( f )= 8 π hf 3 c 3 1 e hf/kT - 1 ,w ( λ )= 8 π hc λ 5 1 e hc/ λ kT - 1 Stefan-Boltzmann’s law for the total power density can be derived from this: P = A σ T 4 . Wien’s law for the maximum can also be derived from this: T λ max = k W . 10.1.2 The Compton effect For the wavelength of scattered light, if light is considered to exist of particles, can be derived: λ ± = λ + h mc (1 - cos θ )= λ + λ C (1 - cos θ ) 10.1.3 Electron diffraction Diffraction of electrons at a crystal can be explained by assuming that particles have a wave character with wavelength λ = h/p . This wavelength is called the Broglie-wavelength. 10.2 Wave functions The wave character of particles is described by a wavefunction ψ . This wavefunction can be described in normal or momentum space. Both de±nitions are each others Fourier transform: Φ (
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Unformatted text preview: k, t ) = 1 h ( x, t )e-ikx dx and ( x, t ) = 1 h ( k, t )e ikx dk These waves dene a particle with group velocity v g = p/m and energy E = h . The wavefunction can be interpreted as a measure for the probability P to nd a particle somewhere (Born): dP = | | 2 d 3 V . The expectation value f of a quantity f of a system is given by: f ( t ) = * f d 3 V , f p ( t ) = * f d 3 V p This is also written as f ( t ) = | f | . The normalizing condition for wavefunctions follows from this: | = | = 1 . 10.3 Operators in quantum physics In quantum mechanics, classical quantities are translated into operators. These operators are hermitian because their eigenvalues must be real: * 1 A 2 d 3 V = 2 ( A 1 ) * d 3 V...
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This note was uploaded on 01/30/2011 for the course PHYSICS 208 taught by Professor Ye during the Spring '10 term at Blinn College.

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