Berechnung der natürlichen Linienbreite auf Grund der Diracschen Lichttheorie

Berechnung der natürlichen Linienbreite auf Grund der Diracschen Lichttheorie

1930 | V. Weisskopf in Göttingen und E. Wigner in Berlin
The natural line width is calculated based on Dirac's light theory. V. Weisskopf and E. Wigner present their findings. The Dirac equations for the interaction between atoms and radiation are solved approximately in a different way than usual. The solutions are valid throughout the time relevant for emission and provide the intensity profile of emission lines. In classical theory, the time dependence of a wave emitted by an oscillator is given by an exponential decay multiplied by a cosine function. Spectral decomposition of this function yields the intensity of light at frequency ν, approximated by a Lorentzian function. The older quantum theory adopted this formula, determining the constant γ, which represents the double half-width. The lifetime τ_A of a state A is the reciprocal of the sum of transition probabilities from A. This lifetime determines the coherence length of emitted lines, implying that the half-width is at least γ_A. For a resonance line, where A can only transition to B via spontaneous emission, γ_A equals the transition probability from A to B. This leads to the formula for the line width, replacing the classical γ with the quantum mechanical γ_A. The line width is then given by a Lorentzian function, where the half-width is γ_A. This implies that all lines from a level are equally broad, determined by the finite lifetime of the wave packet. An alternative view, based on the strict validity of E = hν, leads to the conclusion that energy levels cannot be infinitely sharp. The probability that an atom's energy lies between E and E + ΔE is given by a Lorentzian function, showing that energy levels have a finite width. This approach aligns with Dirac's theory and explains the finite width of energy levels.The natural line width is calculated based on Dirac's light theory. V. Weisskopf and E. Wigner present their findings. The Dirac equations for the interaction between atoms and radiation are solved approximately in a different way than usual. The solutions are valid throughout the time relevant for emission and provide the intensity profile of emission lines. In classical theory, the time dependence of a wave emitted by an oscillator is given by an exponential decay multiplied by a cosine function. Spectral decomposition of this function yields the intensity of light at frequency ν, approximated by a Lorentzian function. The older quantum theory adopted this formula, determining the constant γ, which represents the double half-width. The lifetime τ_A of a state A is the reciprocal of the sum of transition probabilities from A. This lifetime determines the coherence length of emitted lines, implying that the half-width is at least γ_A. For a resonance line, where A can only transition to B via spontaneous emission, γ_A equals the transition probability from A to B. This leads to the formula for the line width, replacing the classical γ with the quantum mechanical γ_A. The line width is then given by a Lorentzian function, where the half-width is γ_A. This implies that all lines from a level are equally broad, determined by the finite lifetime of the wave packet. An alternative view, based on the strict validity of E = hν, leads to the conclusion that energy levels cannot be infinitely sharp. The probability that an atom's energy lies between E and E + ΔE is given by a Lorentzian function, showing that energy levels have a finite width. This approach aligns with Dirac's theory and explains the finite width of energy levels.
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[slides] Berechnung der nat%C3%BCrlichen Linienbreite auf Grund der Diracschen Lichttheorie | StudySpace