In this paper, using the new type of D-dimensional nonperturbative Generalized Uncertainty Principle (GUP) which has predicted both a minimal length uncertainty and a maximal observable momentum,1 first, we obtain the maximally localized states and express their connections to [P. Pedram, Phys. Lett. B 714, 317 (2012)]. Then, in the context of our proposed GUP and using the generalized Schr¨odinger equation, we solve some important problems including particle in a box and one-dimensional hydrogen atom. Next, implying modified Bohr–Sommerfeld quantization, we obtain energy spectra of quantum harmonic oscillator and quantum bouncer. Finally, as an example, we investigate some statistical properties of a free particle, including partition function and internal energy, in the presence of the mentioned GUP.
کلید واژگان :Quantum gravity; generalized uncertainty principle; minimal length uncertainty; maximal momentum; particle in a box; hydrogen atom; Bohr–Sommerfeld quantization; quantum harmonic oscillator; quantum bouncer.
ارزش ریالی : 600000 ریال
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