Mathematical physics

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Mathematical physics
refers to the development of mathematical methods for application to problems in physics.

The Journal of Mathematical Physics defines the field as
"the application of mathematics to problems in physics and
the development of mathematical methods suitable for such applications
and for the formulation of physical theories".[1]

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Following mathematics: the theory of partial differential equation,
variational calculus, Fourier analysis, potential theory, and
vector analysis are perhaps most closely associated with mathematical physics.

These were developed intensively from the second half of the 18th century
(by, for example, D'Alembert, Euler, and Lagrange) until the 1930s.
Physical applications of these developments include hydrodynamics,
celestial mechanics, continuum mechanics, elasticity theory, acoustics,
thermodynamics, electricity, magnetism, and aerodynamics.

The theory of atomic spectra (and, later, quantum mechanics)
developed almost concurrently with some parts of the mathematical fields
of linear algebra, the spectral theory of operators, operator algebras
and more broadly, functional analysis.
Nonrelativistic quantum mechanics includes Schrödinger operators,
and it has connections to atomic and molecular physics.
Quantum information theory is another subspecialty.

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The theory of atomic spectra (and, later, quantum mechanics) developed
almost concurrently with some parts of the mathematical fields of
linear algebra, the spectral theory of operators, operator algebras
and more broadly, functional analysis.

Nonrelativistic quantum mechanics includes Schrödinger operators,
and it has connections to atomic and molecular physics.
Quantum information theory is another subspecialty.

Wiki

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Mathematical physics, Branch of mathematical analysis that emphasizes tools and techniques of
particular use to physicists and engineers.

It focuses on vector spaces, matrix algebra, differential equations
(especially for boundary value problems), integral equations, integral transforms,
infinite series, and complex variables.

Its approach can be tailored to applications in electromagnetism, classical mechanics,
and quantum mechanics.

https://www.britannica.com/science/mathematical-physics