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Archives of physics research

Understanding the decay of atom in quantum theory of radiation using the concept of area

Farzana B. Hazarika, Bidyut Goswami, H. Konwar, Gauranga Dhar Baruah

Published Jan 1, 2012• 0 citations
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Abstract

In the present work we have worked out a vector model for spontaneous emission based on the principle of moving vectors. This simplified approach reflects the work of Weisskopf and Wigner of spontaneous emission

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The Theory of Spontaneous Emission and Manifestation of Fermis Golden Rule

Jyotisman Saikia, B. Goswami, Gauranga Dhar Baruah

In the present work we have worked out a vector model for spontaneous emission based on the principle of moving vectors.This simplified approach reflects the work of Weisskopf and Wigner.Normalized probability of a transition to an upper level versus detuning has been plotted.Further we have shown that the areas which have been generated at phasor diagrams in different values of decay constants for moving vectors are directly proportional to time.This is a manifestation of Fermi's Golden rule.Fermi's Golden Rule in quantum mechanics is well known.But it is for the first time that we have worked out the concept of moving vectors using the transition probabilities and the concept of phasor diagrams to represent the Fermi's Golden rule.

International Journal of Scientific Research in Physics and Applied Sciences•Dec 31, 2018•0 citations

Spectrum in spontaneous emission: Beyond the Weisskopf-Wigner approximation

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The theory of spontaneous emission presented by Weisskopf and Wigner [V. Weisskopf and E. Wigner, Z. Phys. 63, 54 (1930)] provides an excellent approximation of the actual decay that atoms undergo on optically allowed transitions. However, the theory cannot be rigorously correct since it leads to a Lorentzian spectrum that extends to negative frequencies. Within the rotating-wave approximation, we derive a closed-form expression for the spectrum that is valid for all frequencies.

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Emission of Radiation from a System of Many Excited Atoms

V. Ernst, P. Stehle

The Weisskopf-Wigner theory of the natural linewidth of a single isolated atom is extended to a system of $N(\ensuremath{\gg}1)$ identical nonoverlapping atoms which are all in the same excited state at time $t=0$. The positions ${\mathrm{X}}_{1}\ensuremath{\cdots}{\mathrm{X}}_{N}$ of the atoms are assumed to fill a volume $\mathcal{U}$ of given shape and size with macroscopically constant density. Emission of radiation from this system takes place only in the form of one narrow, but nonzero-width, bundle of nearly equal photons, which contains all the emitted radiation. If the density of atoms within $\mathcal{U}$ exceeds a certain threshold, the rate of emission of photons has the form of a typical spike. All effects depend sensitively on the shape and size of $\mathcal{U}$ and on the density of atoms within $\mathcal{U}$, and cannot be explained in conventional terms of spontaneous or stimulated emission of radiation.

Physical Review•Dec 25, 1968•183 citations

Spontaneous emission

P. van der Straten, Harold J. Metcalf

Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.

Cambridge University Press eBooks•Dec 31, 2015•0 citations
In the present work we have worked out a vector model for spontaneous emission based on the principle of moving vectors.This simplified approach reflects the work of Weisskopf and Wigner.Normalized probability of a transition to an upper level versus detuning has been plotted.Further we have shown that the areas which have been generated at phasor diagrams in different values of decay constants for moving vectors are directly proportional to time.This is a manifestation of Fermi's Golden rule.Fermi's Golden Rule in quantum mechanics is well known.But it is for the first time that we have worked out the concept of moving vectors using the transition probabilities and the concept of phasor diagrams to represent the Fermi's Golden rule.
The Weisskopf-Wigner theory of the natural linewidth of a single isolated atom is extended to a system of $N(\ensuremath{\gg}1)$ identical nonoverlapping atoms which are all in the same excited state at time t=0t=0t=0. The positions ${\mathrm{X}}_{1}\ensuremath{\cdots}{\mathrm{X}}_{N}$ of the atoms are assumed to fill a volume U\mathcal{U}U of given shape and size with macroscopically constant density. Emission of radiation from this system takes place only in the form of one narrow, but nonzero-width, bundle of nearly equal photons, which contains all the emitted radiation. If the density of atoms within U\mathcal{U}U exceeds a certain threshold, the rate of emission of photons has the form of a typical spike. All effects depend sensitively on the shape and size of U\mathcal{U}U and on the density of atoms within U\mathcal{U}U, and cannot be explained in conventional terms of spontaneous or stimulated emission of radiation.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.