Translation operator

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Momentum
Quantum mechanics
Quantum state
Unitary operators
Displacement
Momentum operator
Operators

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Kronig-Penney Periodic Potential Model

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Published in Vinod Kumar Khanna, Introductory Nanoelectronics, 2020

Vinod Kumar Khanna

which means that the operators T^,H^ have the same eigenfunction Ψ(x). This allows us to use the eigenfunction of the Hamiltonian operator H^ to determine the eigenvalue of the translation operator T^. Suppose the eigenvalue of the translation operator is γ. Then we can write using eq. (9.22) T^Ψ(x)=Ψ(x+c)=γΨ(x)

Space-time fractional diffusion equation associated with Jacobi expansions

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Published in Applicable Analysis, 2023

Néjib Ben Salem

The convolution of two functions f and g in is given by where denotes the translation operator We note that in [4], the author has proved that the operators , are contractions on .