scholarly journals SUPERSYMMETRY: A CONSEQUENCE OF SMOOTHNESS?

2002 ◽  
Vol 17 (15) ◽  
pp. 2073-2093
Author(s):  
H. B. NIELSEN ◽  
S. PALLUA ◽  
P. PRESTER
Keyword(s):  
Ground State ◽  
Vacuum Energy ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Ground State Properties ◽  
Mechanical Models ◽  
Supersymmetric Theories

The consequences of certain simple assumptions like smoothness of ground state properties and vanishing of the vacuum energy (at least perturbatively) are explored. It would be interesting from the point of view of building realistic theories to obtain these properties without supersymmetry. Here we show, however, at least in some quantum mechanical models, that these simple assumptions lead to supersymmetric theories.

scholarly journals QUANTUM LIE SYSTEMS AND INTEGRABILITY CONDITIONS

2009 ◽  
Vol 06 (08) ◽  
pp. 1235-1252 ◽  
Author(s):  
JOSÉ F. CARIÑENA ◽  
JAVIER DE LUCAS
Keyword(s):  
Quantum Mechanics ◽  
Differential Equations ◽  
Geometric Theory ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Integrable Quantum ◽  
Systems Of Differential Equations ◽  
Integrability Conditions ◽  
Mechanical Models ◽  
Lie Systems

The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analyzed from a geometric perspective. In this paper we use both developments to obtain a geometric theory of integrability in Quantum Mechanics and we use it to provide a series of non-trivial integrable quantum mechanical models and to recover some known results from our unifying point of view.

Ground-state properties of the retinal molecule: from quantum mechanical to classical mechanical computations of retinal proteins

2011 ◽  
Vol 130 (4-6) ◽  
pp. 1169-1183 ◽  
Author(s):  
Ana-Nicoleta Bondar ◽  
Michaela Knapp-Mohammady ◽  
Sándor Suhai ◽  
Stefan Fischer ◽  
Jeremy C. Smith
Keyword(s):  
Ground State ◽  
Quantum Mechanical ◽  
Ground State Properties ◽  
Retinal Proteins

scholarly journals Models for the BPS Berry connection

2020 ◽  
pp. 2150007
Author(s):  
Satoshi Ohya
Keyword(s):  
Ground State ◽  
Monotonic Function ◽  
Quantum Mechanical ◽  
Model Parameters ◽  
State Sector ◽  
Yang Mills ◽  
Systematic Construction ◽  
Mechanical Models

Motivated by the Nahm’s construction, in this paper, we present a systematic construction of Schrödinger Hamiltonians for a spin-1/2 particle where the Berry connection in the ground-state sector becomes the Bogomolny–Prasad–Sommerfield (BPS) monopole of SU(2) Yang–Mills–Higgs theory. Our construction enjoys a single arbitrary monotonic function, thereby creating infinitely many quantum-mechanical models that simulate the BPS monopole in the space of model parameters.

The Riccati–Padé quantization method for one-dimensional quantum-mechanical models

1996 ◽  
Vol 74 (9-10) ◽  
pp. 697-700 ◽  
Author(s):  
Francisco M. Fernández ◽  
R. H. Tipping
Keyword(s):  
Ground State ◽  
Logarithmic Derivative ◽  
Quantum Mechanical ◽  
Quantization Method ◽  
Anharmonic Oscillators ◽  
Eigenvalues And Eigenfunctions ◽  
One Dimensional ◽  
Continuum States ◽  
Separable Models ◽  
Mechanical Models

We improve on a previously developed method for the calculation of accurate eigenvalues and eigenfunctions of separable models in quantum mechanics. It consists of the approximation of the logarithmic derivative of the eigenfunction by means of a rational function or Padé approximant. Here we modify the approach by the separation of the function just mentioned into its odd and even parts, thus making the procedure more efficient for treating asymmetric one-dimensional potentials. We obtain the ground-state eigenvalue of anharmonic oscillators with one and two wells and the lowest resonances of anharmonic oscillators that support only continuum states.

Ground state molecular parameters of phosphine, PH3, from the simultaneous analysis of the high-resolution infrared, microwave and submillimeterwave spectra

1985 ◽  
Vol 50 (11) ◽  
pp. 2480-2492 ◽  
Author(s):  
Soňa Přádná ◽  
Dušan Papoušek ◽  
Jyrki Kauppinen ◽  
Sergei P. Belov ◽  
Andrei F. Krupnov ◽  
...  
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Ground State ◽  
Unitary Transformation ◽  
Point Of View ◽  
Acoustic Detection ◽  
Molecular Parameters ◽  
Microwave Spectrometer ◽  
Fourier Transform Spectra ◽  
First Time

Fourier transform spectra of the ν2 band of PH3 have been remeasured with 0.0045 cm-1 resolution. Ground state combination differences from these data have been fitted simultaneously with the microwave and submillimeterwave data to determine the ground state spectroscopical parameters of PH3 including the parameters of the Δk = ± 3n interactions. The correlation between the latter parameters has been discussed from the point of view of the existence of two equivalent effective rotational operators which are related by a unitary transformation. The ΔJ = 0, +1, ΔK = 0 (A1 ↔ A2, E ↔ E) rotational transitions in the ν2 and ν4 states have been measured for the first time by using a microwave spectrometer and a radiofrequency spectrometer with acoustic detection.

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

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