scholarly journals Quantum Tunneling in Deformed Quantum Mechanics with Minimal Length

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaobo Guo ◽  
Bochen Lv ◽  
Jun Tao ◽  
Peng Wang
Keyword(s):  
Quantum Mechanics ◽  
Atomic Physics ◽  
Quantum Tunneling ◽  
Turning Point ◽  
Minimal Length ◽  
Wkb Approximation ◽  
Potential Barriers ◽  
Connection Formula ◽  
Length Effects ◽  
Tunneling Rates

In the deformed quantum mechanics with a minimal length, one WKB connection formula through a turning point is derived. We then use it to calculate tunneling rates through potential barriers under the WKB approximation. Finally, the minimal length effects on two examples of quantum tunneling in nuclear and atomic physics are discussed.

scholarly journals Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Jun Tao ◽  
Peng Wang ◽  
Haitang Yang
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Statistical Physics ◽  
Turning Point ◽  
Minimal Length ◽  
Jacobi Method ◽  
Homogeneous Field ◽  
Quantization Rule ◽  
Connection Formula ◽  
Forbidden Region

In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up toOβ2. We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.

scholarly journals COMPLEX-TIME APPROACH FOR SEMICLASSICAL QUANTUM TUNNELING

1995 ◽  
Vol 10 (15n16) ◽  
pp. 1135-1142 ◽  
Author(s):  
HIDEAKI AOYAMA ◽  
TOSHIYUKI HARANO
Keyword(s):  
Quantum Mechanics ◽  
Green Function ◽  
Quantum Tunneling ◽  
Turning Points ◽  
Wkb Approximation ◽  
Reduction Formula ◽  
Complex Time ◽  
One Dimensional

The complex-time method for quantum tunneling is studied. In one-dimensional quantum mechanics, we construct a reduction formula for a Green function in the number of turning points based on the WKB approximation. This formula yields a series, which can be interpreted as a sum over the complex-time paths. The weights of the paths are determined.

Dualism QM and GR

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Noncommutative Geometry ◽  
Quantum Tunneling ◽  
Closed Surface ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Surface Integral ◽  
Definition Of

Quantum tunneling of noncommutative geometry gives the definition of time in the form of holography, that is, in the form of a closed surface integral. Ultimately, the holography of time shows the dualism between quantum mechanics and the general theory of relativity.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

Revision, Analogy, and the “Problem of Reality” in Michael Frayn’s Copenhagen and Human Touch

Modern Drama ◽  
2021 ◽  
Vol 64 (2) ◽  
pp. 173-196
Author(s):  
Derek Gingrich
Keyword(s):  
Quantum Mechanics ◽  
Atomic Physics ◽  
Human Experience ◽  
Pivotal Role ◽  
Central Question ◽  
Language Identity ◽  
Working Through ◽  
Human Touch

Published eight years after the premiere of Copenhagen, his celebrated play about atomic physics, Michael Frayn’s Human Touch (2006) reflects on the epistemological and phenomenological implications of human experience, syntax, and quantum mechanics. Summarily, Frayn posits that reality’s fundamental indeterminacy makes thought, language, identity, culture, and experience possible at all. The book echoes more than Copenhagen’s themes, however, and the pair’s structural similarities invite readers to rethink Copenhagen as a piece of philosophical theatre. The play foregrounds the process of drafting and redrafting, and it stands as a draft of the ideas in the book that soon followed. The book follows suit as it drafts and redrafts its central question through its prodigious length. In conversation with Human Touch, we can read Copenhagen as an exploration of our ability to forge connections between otherwise disparate features of reality (including quantum mechanics). More crucially, Copenhagen demonstrates the pivotal role that theatre plays in the indeterminate epistemology that Frayn espouses in Human Touch. In doing so, Copenhagen embodies an earlier draft of the epistemology Frayn later explicates in the book. In other words, Copenhagen represents a rare example of a thinker working through philosophical ideas on stage before committing them to an argument.

scholarly journals Quantum Tunneling Rates of Gas-Phase Reactions from On-the-Fly Instanton Calculations

2016 ◽  
Vol 7 (21) ◽  
pp. 4374-4379 ◽  
Author(s):  
Adrian N. Beyer ◽  
Jeremy O. Richardson ◽  
Peter J. Knowles ◽  
Judith Rommel ◽  
Stuart C. Althorpe
Keyword(s):  
Gas Phase ◽  
Quantum Tunneling ◽  
Gas Phase Reactions ◽  
Tunneling Rates
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