Quantum Tunneling In Deformed Quantum Mechanics with Minimal Length

WKB Approximation for a Deformed Schrodinger-like Equation and its Applications to Quasinormal Modes of Black Holes and Quantum Cosmology

“…In the context of both GUP and MDR, the deformed Bohr-Sommerfeld quantization rule was used to compute the number of quantum states to find the entanglement entropy of black holes in the brick wall model [5][6][7]. In [3,4], we found the WKB connection formulas and proved the deformed Bohr-Sommerfeld quantization rule and tunneling rate formula for the g (x) = √ 1 + x 2 case. In this paper, we will consider the case with an arbitrary function g (x), for which the WKB connection formulas, Bohr-Sommerfeld quantization rule and tunneling rate formula are obtained.…”

“…For example, in the framework of GUP, the WKB wave functions were obtained in [1]. Moreover, the deformed Bohr-Sommerfeld quantization rule and tunneling rate formula were used to calculate bound states of Harmonic oscillators and Hydrogen atoms [1], α-decay [2,3], quantum cosmogenesis [2], the volume of a phase cell [4], and electron emissions [3], for some specific function g (x). In the context of both GUP and MDR, the deformed Bohr-Sommerfeld quantization rule was used to compute the number of quantum states to find the entanglement entropy of black holes in the brick wall model [5][6][7].…”