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Bargmann's limit

Index Bargmann's limit

In quantum mechanics, Bargmann's limit, named for Valentine Bargmann, provides an upper bound on the number N_\ell of bound states with azimuthal quantum number \ell in a system with central potential V. It takes the form This limit is the best possible upper bound in such a way that for a given \ell, one can always construct a potential V_\ell for which N_\ell is arbitrarily close to this upper bound. [1]

Table of Contents

  1. 10 relations: Azimuthal quantum number, Bound state, Dirac delta function, Julian Schwinger, Quantum mechanics, Schrödinger equation, Sturm–Picone comparison theorem, Upper and lower bounds, Valentine Bargmann, Variation of parameters.

Azimuthal quantum number

In quantum mechanics, the azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes aspects of the angular shape of the orbital.

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Bound state

A bound state is a composite of two or more fundamental building blocks, such as particles, atoms, or bodies, that behaves as a single object and in which energy is required to split them.

See Bargmann's limit and Bound state

Dirac delta function

In mathematical analysis, the Dirac delta function (or distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one.

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Julian Schwinger

Julian Seymour Schwinger (February 12, 1918 – July 16, 1994) was a Nobel Prize-winning American theoretical physicist.

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Quantum mechanics

Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms.

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Schrödinger equation

The Schrödinger equation is a partial differential equation that governs the wave function of a quantum-mechanical system. Bargmann's limit and Schrödinger equation are quantum mechanics.

See Bargmann's limit and Schrödinger equation

Sturm–Picone comparison theorem

In mathematics, in the field of ordinary differential equations, the Sturm–Picone comparison theorem, named after Jacques Charles François Sturm and Mauro Picone, is a classical theorem which provides criteria for the oscillation and non-oscillation of solutions of certain linear differential equations in the real domain.

See Bargmann's limit and Sturm–Picone comparison theorem

Upper and lower bounds

In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is every element of.

See Bargmann's limit and Upper and lower bounds

Valentine Bargmann

Valentine "Valya" Bargmann (April 6, 1908 – July 20, 1989) was a German-American mathematician and theoretical physicist.

See Bargmann's limit and Valentine Bargmann

Variation of parameters

In mathematics, variation of parameters, also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations.

See Bargmann's limit and Variation of parameters

References

[1] https://en.wikipedia.org/wiki/Bargmann's_limit