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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 ...
Prism spectacles with a single prism perform a relative displacement of the two eyes, thereby correcting eso-, exo, hyper- or hypotropia. In contrast, spectacles with prisms of equal power for both eyes, called yoked prisms (also: conjugate prisms, ambient lenses or performance glasses) shift the visual field of both eyes to the same extent.
Prentice's rule, named so after the optician Charles F. Prentice, is a formula used to determine the amount of induced prism in a lens: = where: P is the amount of prism correction (in prism dioptres) c is decentration (the distance between the pupil centre and the lens's optical centre, in millimetres)
Mass number. A = (Relative) atomic mass = Mass number = Sum of protons and neutrons. N = Number of neutrons. Z = Atomic number = Number of protons = Number of electrons. A = Z + N {\displaystyle A=Z+N\,\!} Mass in nuclei. M'nuc = Mass of nucleus, bound nucleons. MΣ = Sum of masses for isolated nucleons.
In a prism, dispersion causes different colors to refract at different angles, splitting white light into a rainbow of colors. In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium.
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.
Following is a list of the frequently occurring equations in the theory of special relativity.
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun.
This equation occurs in many applications of basic physics. The following equations start from the general equations of linear motion: d ( t ) = d 0 + v 0 t + 1 2 a t 2 {\displaystyle d(t)=d_{0}+v_{0}t+{1 \over 2}at^{2}}