DOIONLINE 
DOIONLINE Publish In |
International Journal of Advances in Science, Engineering and Technology(IJASEAT)-IJASEAT |
 Journal Home Volume Issue |
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Issue |
Volume-10,Issue-3 ( Jul, 2022 ) | |||||||||
Paper Title |
Thermodynamic Potentials Generalized from a 𝜆-Deformed Exponential Function | |||||||||
Author Name |
Jj Peña, J Morales, G Ovando | |||||||||
Affilition |
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Pages |
156-161 | |||||||||
Abstract |
Abstract - In the transformation of the effective Hamiltonian for the case of a spatially dependent mass, into its canonical form, a generalized (𝜆-deformed) Hermitian linear momentum operator p_λis deduced. Added to this, a spatial canonical transformation x_λto solve the resulting differential equation leads to a 𝜆-deformed quantum mechanics.In this scenario it is possible to propose a 𝜆-deformed exponential function 〖exp〗_λ (x)=exp(x_λ) and its corresponding𝜆-deformed logarithmic partner〖ln〗_λ (x).From these results, and the definition of the internal energy U=-k ∂/∂β ln(Z), it is straightforward to get the generalized internal energyU_λ=-k ∂/∂β 〖ln〗_λ (Z_λ ) which enables a natural generalization of others thermodynamic functions such as the EntropyS_λ, the Helmholtz free energy F_λ and the heat capacity C_λ.Some particular mass distributionsm(λ;x) are used as example to illustrate the proposal. Besides, in the case of m(λ;x)=m_0 〖(1+λx)〗^(-2) our proposal leads straightforwardly to the Tsallis results obtained by solving a variational problem with suitable Lagrange parameters. Keywords - Schrödinger Equation, Position-dependent Mass, Generalized Exponential Function, Internal Energy, Thermodynamic Functions. | |||||||||
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