Hermite polynomials and Fibonacci oscillators
Copyright policy )Hermite polynomials and Fibonacci oscillators
We compute the (q1, q2)-deformed Hermite polynomials by replacing the quantum harmonic oscillator problem to Fibonacci oscillators. We do this by applying the (q1, q2)-extension of Jackson derivative. The deformed energy spectrum is also found in terms of these parameters. We conclude that the deformation is more effective in higher excited states. We conjecture that this achievement may find applications in the inclusion of disorder and impurity in quantum systems. The ordinary quantum mechanics is easily recovered as q1 = 1 and q2 → 1 or vice versa.
High Energy Physics - Theory, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, General topics in linear spectral theory for PDEs, Quantum state estimation, approximate cloning, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), High Energy Physics - Theory (hep-th), Fibonacci and Lucas numbers and polynomials and generalizations, Quantum Physics (quant-ph), Condensed Matter - Statistical Mechanics, Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
High Energy Physics - Theory, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, General topics in linear spectral theory for PDEs, Quantum state estimation, approximate cloning, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), High Energy Physics - Theory (hep-th), Fibonacci and Lucas numbers and polynomials and generalizations, Quantum Physics (quant-ph), Condensed Matter - Statistical Mechanics, Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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