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Summarized below are the various forms the Hamiltonian takes, with the corresponding Schrödinger equations and forms of wavefunction solutions. Notice in the case of one spatial dimension, for one particle, the partial derivative reduces to an ordinary derivative .
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak ...
The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system. The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave.
Introduction to the concept. Quantum tunnelling falls under the domain of quantum mechanics. To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill. Quantum mechanics and classical mechanics differ in their treatment of this scenario.
Gibbs paradox. In statistical mechanics, a semi-classical derivation of entropy that does not take into account the indistinguishability of particles yields an expression for entropy which is not extensive (is not proportional to the amount of substance in question).
Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
In nuclear physics and nuclear chemistry, the fission barrier is the activation energy required for a nucleus of an atom to undergo fission. This barrier may also be defined as the minimum amount of energy required to deform the nucleus to the point where it is irretrievably committed to the fission process. The energy to overcome this barrier ...
In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to electron spin and relativistic corrections to the non-relativistic Schrödinger equation.
Surface plasmon resonance ( SPR) is a phenomenon that occurs where electrons in a thin metal sheet become excited by light that is directed to the sheet with a particular angle of incidence, and then travel parallel to the sheet. Assuming a constant light source wavelength and that the metal sheet is thin, the angle of incidence that triggers ...
Under the usual free/interaction decomposition, which is suitable for low energies, the free fields obey the following equations: The fermion field ψ satisfies the Dirac equation ; ( i ℏ γ μ ∂ μ − m f c ) ψ f = 0 {\displaystyle (i\hbar \gamma ^{\mu }\partial _{\mu }-m_{\rm {f}}c)\psi _{\rm {f}}=0} for each type f {\displaystyle f} of ...