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Transition Dipole Moment
The transition dipole moment or transition moment, usually denoted \mathbf_ for a transition between an initial state, m, and a final state, n, is the electric dipole moment associated with the transition between the two states. In general the transition dipole moment is a complex vector quantity that includes the phase factors associated with the two states. Its direction gives the polarization of the transition, which determines how the system will interact with an electromagnetic wave of a given polarization, while the square of the magnitude gives the strength of the interaction due to the distribution of charge within the system. The SI unit of the transition dipole moment is the Coulomb-meter (Cm); a more conveniently sized unit is the Debye (D). Definition A single charged particle For a transition where a single charged particle changes state from , \psi_a \rangle to , \psi_b \rangle , the transition dipole moment \text is (\text a \rightarrow b) = \langl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absorption (electromagnetic Radiation)
In physics, absorption of electromagnetic radiation is how matter (typically electrons bound in atoms) takes up a photon's energy—and so transforms electromagnetic energy into internal energy of the absorber (for example, thermal energy). A notable effect of the absorption of electromagnetic radiation is attenuation of the radiation; attenuation is the gradual reduction of the intensity of light waves as they propagate through a medium. Although the absorption of waves does not usually depend on their intensity (linear absorption), in certain conditions (optics) the medium's transparency changes by a factor that varies as a function of wave intensity, and saturable absorption (or nonlinear absorption) occurs. Quantifying absorption Many approaches can potentially quantify radiation absorption, with key examples following. * The absorption coefficient along with some closely related derived quantities * The attenuation coefficient (NB used infrequently with meaning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wigner–Eckart Theorem
The Wigner–Eckart theorem is a theorem of representation theory and quantum mechanics. It states that matrix elements of spherical tensor operators in the basis of angular momentum eigenstates can be expressed as the product of two factors, one of which is independent of angular momentum orientation, and the other a Clebsch–Gordan coefficient. The name derives from physicists Eugene Wigner and Carl Eckart, who developed the formalism as a link between the symmetry transformation groups of space (applied to the Schrödinger equations) and the laws of conservation of energy, momentum, and angular momentum.Eckart Biography – The National Academies Press. Mathematically, the Wigner–Eckart theorem is generally stated in the following way. Given a tensor operator and two states of angular mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Dipole Transition
An electric dipole transition is the dominant effect of an interaction of an electron in an atom with the electromagnetic field. Following reference, consider an electron in an atom with quantum Hamiltonian H_0 , interacting with a plane electromagnetic wave : (,t)=E_0 \cos(ky-\omega t), \ \ \ (,t)=B_0 \cos(ky-\omega t). Write the Hamiltonian of the electron in this electromagnetic field as : H(t) \ = \ H_0 + W(t). Treating this system by means of time-dependent perturbation theory, one finds that the most likely transitions of the electron from one state to the other occur due to the summand of W(t) defined as : W_\mathrm(t) = \frac p_z \sin \omega t, \, where q and m_e are the charge and mass of a bare electron. Electric dipole transitions are the transitions between energy levels in the system with the Hamiltonian H_0 + W_\mathrm(t) . Between certain electron states the electric dipole transition rate may be zero due to one or more selection rules, particular ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Selection Rule
In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, in atomic nucleus, atomic nuclei, and so on. The selection rules may differ according to the technique used to observe the transition. The selection rule also plays a role in chemical reactions, where some are formally spin-forbidden reactions, that is, reactions where the spin state changes at least once from Reagent, reactants to Product (chemistry), products. In the following, mainly atomic and molecular transitions are considered. Overview In quantum mechanics the basis for a spectroscopic selection rule is the value of the ''transition moment integral'' :m_ = \int \psi_1^* \, \mu \, \psi_2 \, \mathrm\tau, where \psi_1 and \psi_2 are the wave functions of the two states, "state 1" and "state 2", involved in the transition, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity (physics)
In physics, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point reflection): \mathbf: \beginx\\y\\z\end \mapsto \begin-x\\-y\\-z\end. It can also be thought of as a test for chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. All fundamental interactions of elementary particles, with the exception of the weak interaction, are symmetric under parity transformation. As established by the Wu experiment conducted at the US National Bureau of Standards by Chinese-American scientist Chien-Shiung Wu, the weak interaction is chiral and thus provides a means for probing chirality in physics. In her experiment, Wu took advantage of the controlling role of weak interactions in radioactive decay of atomic isotopes to establish the chirality of the weak f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. the other being Derivative, differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. A definite integral computes the signed area of the region in the plane that is bounded by the Graph of a function, graph of a given Function (mathematics), function between two points in the real line. Conventionally, areas above the horizontal Coordinate axis, axis of the plane are positive while areas below are n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Even And Odd Functions
In mathematics, an even function is a real function such that f(-x)=f(x) for every x in its domain. Similarly, an odd function is a function such that f(-x)=-f(x) for every x in its domain. They are named for the parity of the powers of the power functions which satisfy each condition: the function f(x) = x^n is even if ''n'' is an even integer, and it is odd if ''n'' is an odd integer. Even functions are those real functions whose graph is self-symmetric with respect to the and odd functions are those whose graph is self-symmetric with respect to the origin. If the domain of a real function is self-symmetric with respect to the origin, then the function can be uniquely decomposed as the sum of an even function and an odd function. Early history The concept of even and odd functions appears to date back to the early 18th century, with Leonard Euler playing a significant role in their formalization. Euler introduced the concepts of even and odd functions (using La ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. the other being Derivative, differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. A definite integral computes the signed area of the region in the plane that is bounded by the Graph of a function, graph of a given Function (mathematics), function between two points in the real line. Conventionally, areas above the horizontal Coordinate axis, axis of the plane are positive while areas below are n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscillator Strength
In spectroscopy, oscillator strength is a dimensionless quantity that expresses the probability of absorption or emission of electromagnetic radiation in transitions between energy levels of an atom or molecule. For example, if an emissive state has a small oscillator strength, nonradiative decay will outpace radiative decay. Conversely, "bright" transitions will have large oscillator strengths. The oscillator strength can be thought of as the ratio between the quantum mechanical transition rate and the classical absorption/emission rate of a single electron oscillator with the same frequency as the transition. Theory An atom or a molecule can absorb light and undergo a transition from one quantum state to another. The oscillator strength f_ of a transition from a lower state , 1\rangle to an upper state , 2\rangle may be defined by : f_ = \frac\frac(E_2 - E_1) \sum_ , \langle 1 m_1 , R_\alpha , 2 m_2 \rangle , ^2, where m_e is the mass of an electron and \hbar is the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emission (electromagnetic Radiation)
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to electrons making a transition from a high energy state to a lower energy state. The photon energy of the emitted photons is equal to the energy difference between the two states. There are many possible electron transitions for each atom, and each transition has a specific energy difference. This collection of different transitions, leading to different radiated wavelengths, make up an emission spectrum. Each element's emission spectrum is unique. Therefore, spectroscopy can be used to identify elements in matter of unknown composition. Similarly, the emission spectra of molecules can be used in chemical analysis of substances. Emission In physics, emission is the process by which a higher energy quantum mechanical state of a particle becomes converted to a lower one through the emission of a photon, resulting in the production of light ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can move no faster than the speed of light measured in vacuum. The photon belongs to the class of boson particles. As with other elementary particles, photons are best explained by quantum mechanics and exhibit wave–particle duality, their behavior featuring properties of both waves and particles. The modern photon concept originated during the first two decades of the 20th century with the work of Albert Einstein, who built upon the research of Max Planck. While Planck was trying to explain how matter and electromagnetic radiation could be in thermal equilibrium with one another, he proposed that the energy stored within a material object should be regarded as composed of an integer number of discrete, equal-sized parts. To explain the pho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
