Supersymmetric Quantum Mechanics, Excited State Energies and Wave Functions, and the Rayleigh−Ritz Variational Principle: A Proof of Principle Study†

2009 ◽  
Vol 113 (52) ◽  
pp. 15257-15264 ◽  
Author(s):  
Donald J. Kouri ◽  
Thomas Markovich ◽  
Nicholas Maxwell ◽  
Eric R. Bittner
Keyword(s):  
Quantum Mechanics ◽  
Excited State ◽  
Variational Principle ◽  
Wave Functions ◽  
Supersymmetric Quantum Mechanics ◽  
Proof Of Principle

Asymptotic Functional Form Preservation Method with Supersymmetric Quantum Mechanics for Anharmonic Oscillators

2016 ◽  
Vol 69 (9) ◽  
pp. 950 ◽  
Author(s):  
Chia-Chun Chou ◽  
Ching-Teh Li
Keyword(s):  
Quantum Mechanics ◽  
Excited State ◽  
Series Expansion ◽  
Functional Form ◽  
Full Range ◽  
Supersymmetric Quantum Mechanics ◽  
Anharmonic Oscillators ◽  
Approximate Analytical Expression ◽  
Preservation Method ◽  
Functional Forms

The asymptotic functional form preservation method is developed in the framework of supersymmetric quantum mechanics to obtain the energies and wave functions of anharmonic oscillators. For each of the ground states in the hierarchy of supersymmetric partner Hamiltonians, we derive a series expansion of the superpotential for . Employing a transformation containing an unphysical parameter, we convert the series expansion of the superpotential into a new series expansion applicable to all the range of x. The unphysical parameter is determined by the principle of minimal sensitivity. Requiring the preservation of the correct asymptotic functional form of the full-range series expansion as x tends to infinity, we obtain the ground and excited state energies. The truncated full-range series expansion for the superpotential provides an approximate analytical expression for the wave function. In addition, several ansatz functional forms are also proposed for the superpotential to obtain the ground and excited state energies with high accuracy. Excellent computational results for the anharmonic oscillator demonstrate that the method proposed here is suitable for solving similar quantum mechanical problems.

scholarly journals HIGHER-ORDER SUSY, EXACTLY SOLVABLE POTENTIALS, AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS

2011 ◽  
Vol 26 (25) ◽  
pp. 1843-1852 ◽  
Author(s):  
C. QUESNE
Keyword(s):  
Quantum Mechanics ◽  
Orthogonal Polynomials ◽  
Higher Order ◽  
Wave Functions ◽  
Supersymmetric Quantum Mechanics ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Exceptional Orthogonal Polynomials

Exactly solvable rationally-extended radial oscillator potentials, whose wave functions can be expressed in terms of Laguerre-type exceptional orthogonal polynomials, are constructed in the framework of kth-order supersymmetric quantum mechanics, with special emphasis on k = 2. It is shown that for μ = 1, 2, and 3, there exist exactly μ distinct potentials of μth type and associated families of exceptional orthogonal polynomials, where μ denotes the degree of the polynomial gμ arising in the denominator of the potentials.

Visualization and Manipulation of Molecular Motion in Solid State through Photo-Induced Clusteroluminescence

2019 ◽  
Author(s):  
Haoke Zhang ◽  
Lili Du ◽  
Lin Wang ◽  
Junkai Liu ◽  
Qing Wan ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Excited State ◽  
Solid State ◽  
Light Source ◽  
Molecular Motion ◽  
Molecular Machine ◽  
Conjugated Molecules ◽  
Time Resolved ◽  
Packing Structure ◽  
New Strategy

<p>Building molecular machine has long been a dream of scientists as it is expected to revolutionize many aspects of technology and medicine. Implementing the solid-state molecular motion is the prerequisite for a practical molecular machine. However, few works on solid-state molecular motion have been reported and it is almost impossible to “see” the motion even if it happens. Here the light-driven molecular motion in solid state is discovered in two non-conjugated molecules <i>s</i>-DPE and <i>s</i>-DPE-TM, resulting in the formation of excited-state though-space complex (ESTSC). Meanwhile, the newly formed ESTSC generates an abnormal visible emission which is termed as clusteroluminescence. Notably, the original packing structure can recover from ESTSC when the light source is removed. These processes have been confirmed by time-resolved spectroscopy and quantum mechanics calculation. This work provides a new strategy to manipulate and “see” solid-state molecular motion and gains new insights into the mechanistic picture of clusteroluminescence.<br></p>

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

scholarly journals ABCD of ’t Hooft operators

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Takuya Okuda ◽  
Yutaka Yoshida
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Type Ii ◽  
Expectation Values ◽  
String Theories

Abstract We compute by supersymmetric localization the expectation values of half-BPS ’t Hooft line operators in $$ \mathcal{N} $$ N = 2 U(N ), SO(N ) and USp(N ) gauge theories on S1 × ℝ3 with an Ω-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the ’t Hooft operators using branes and orientifolds in type II string theories.

scholarly journals Local G2-manifolds, Higgs bundles and a colored quantum mechanics

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Max Hübner
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Higgs Bundle ◽  
Higgs Bundles ◽  
View Point ◽  
Yang Mills ◽  
G2 Manifolds ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

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