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Wu–Sprung Potential
In mathematical physics, the Wu–Sprung potential, named after Hua Wu and Donald Sprung, is a Potential, potential function in one dimension inside a Hamiltonian mechanics#Mathematical formalism, Hamiltonian H = p^2 + f(x) with the potential defined by solving a non-linear integral equation defined by the Bohr–Sommerfeld quantization conditions involving the spectral staircase, the energies E_n and the potential f(x) . \oint p \, dq =2 \pi n(E)= 4\int_0^a dx \sqrt here is a classical Stationary point, turning point so E = f(a) = f(-a) , the quantum energies of the model are the roots of the Riemann Xi function \xi = 0 and f(x)=f(-x) . In general, although Wu and Sprung considered only the smooth part, the potential is defined implicitly by f^(x)= \sqrt \pi \fracN(x) ; with being the eigenvalue staircase N(x) = \sum_^\infty H(x - E_) and is the Heaviside step function. For the case of the Riemann hypothesis, Riemann zeros Wu and Sprung and others have shown that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics is the development of mathematics, 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". An alternative definition would also include those mathematics that are inspired by physics, known as physical mathematics. Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical parts of our world. Classical mechanics Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of Lagrangian mechanics and Hamiltonian mechanics (including both approaches in the presence of constraints). Both formulations are embodied in analytical mechanics and lead ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
