Seeley–DeWitt expansion of scattering phase shift

In this paper, we use the Seeley–DeWitt expansion of heat kernel method in quantum field theory to give an explicit expression of the perturbation expansion for the scattering phase shift for three-dimensional spherically symmetric potential scattering in quantum mechanics. The spectral function is...

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Bibliographic Details
Published in:European physical journal plus 2022-10, Vol.137 (10), p.1140, Article 1140
Main Authors: Liu, Yuan-Yuan, Chen, Yu-Jie, Li, Shi-Lin, Li, Wen-Du, Dai, Wu-Sheng
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Approximation
Atomic
Black holes
Complex Systems
Condensed Matter Physics
Eigenvalues
Hamiltonian functions
Mathematical and Computational Physics
Methods
Molecular
Operators (mathematics)
Optical and Plasma Physics
Phase shift
Physics
Physics and Astronomy
Quantum field theory
Quantum mechanics
Quantum theory
Regular Article
Scattering
Statistical mechanics
Theoretical
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Summary:In this paper, we use the Seeley–DeWitt expansion of heat kernel method in quantum field theory to give an explicit expression of the perturbation expansion for the scattering phase shift for three-dimensional spherically symmetric potential scattering in quantum mechanics. The spectral function is defined by the eigenproblem of an operator, and the spectral functions are related by transforms. The heat kernel and the scattering phase shift are both spectral functions of the Hamiltonian. By a transform between the heat kernel and the scattering phase shift, we convert the Seeley–DeWitt expansion of heat kernels to an expansion of scattering phase shifts up to the first two orders.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-022-03380-5