Quasi-bound Energy Levels Research Articles

Effects of magnetic field on quasi-bound energy levels of GaAs-AlGaAs coupled quantum well

Effects of magnetic field on quasi-bound energy levels of GaAs-AlGaAs coupled quantum well

Transcendental equation calculated analytically obeyed by quasi-bound energy levels of quantum well and resonant transmission peaks

Transcendental equation calculated analytically obeyed by quasi-bound energy levels of quantum well and resonant transmission peaks

Universal few-body physics and cluster formation

A recent rejuvenation of experimental and theoretical interest in the physics of few- body systems has provided deep, fundamental insights into a broad range of problems. Few-body physics is a cross-cutting discipline not restricted to conventional subject ar- eas such as nuclear physics or atomic or molecular physics. To a large degree, the recent explosion of interest in this subject has been sparked by dramatic enhancements of experimental capabilities in ultracold atomic systems over the past decade, which now permit atoms and molecules to be explored deep in the quantum mechanical limit with controllable two-body interactions. This control, typically enabled by magnetic or electromagnetically-dressed Fano-Feshbach resonances, allows in particular access to the range of universal few-body physics, where two-body scattering lengths far exceed all other length scales in the problem. The Efimov effect, where 3 particles experienc- ing short-range interactions can counterintuitively exhibit an infinite number of bound or quasi-bound energy levels, is the most famous example of universality. Tremendous progress in the field of universal Efimov physics has taken off, driven particularly by a combination of experimental and theoretical studies in the past decade, and prior to the first observation in 2006, by an extensive set of theoretical studies dating back to 1970. Because experimental observations of Efimov physics have usually relied on resonances or interference phenomena in three-body recombination, this connects naturally with the processes of molecule formation in a low temperature gas of atoms or nucleons, and more generally with N-body recombination processes. Some other topics not closely related to the Efimov effect are also reviewed in this article, including ...

New quasibound states of the compound nucleus inα-particle capture by the nucleus

We generalize the theory of nuclear decay and capture of Gamow that is based on tunneling through the barrier and internal oscillations inside the nucleus. In our formalism an additional factor is obtained, which describes distribution of the wave function of the $\alpha$ particle inside the nuclear region. We discover new most stable states (called quasibound states) of the compound nucleus (CN) formed during the capture of $\alpha$ particle by the nucleus. With a simple example, we explain why these states cannot appear in traditional calculations of the $\alpha$ capture cross sections based on monotonic penetrabilities of a barrier, but they appear in a complete description of the evolution of the CN. Our result is obtained by a complete description of the CN evolution, which has the advantages of (1) a clear picture of the formation of the CN and its disintegration, (2) a detailed quantum description of the CN, (3) tests of the calculated amplitudes based on quantum mechanics (not realized in other approaches), and (4) high accuracy of calculations (not achieved in other approaches). These peculiarities are shown with the capture reaction of $\alpha + ^{44}{\rm Ca}$. We predict quasibound energy levels and determine fusion probabilities for this reaction. The difference between our approach and theory of quasistationary states with complex energies applied for the $\alpha$ capture is also discussed. We show (1) that theory does not provide calculations for the cross section of $\alpha$ capture (according to modern models of the $\alpha$ capture), in contrast with our formalism, and (2) these two approaches describe different states of the $\alpha$ capture (for the same $\alpha$-nucleus potential).

Conductance microscopy of quantum dots weakly or strongly coupled to the conducting channel

We consider scanning gate conductance microscopy of an open quantum dot that is connected to the conducting channel using the wave function description of the quantum transport and a finite difference approach. We discuss the information contained in conductance (G) maps. We demonstrate that the maps for a delta-like potential perturbation exactly reproduce the local density of states for a quantum dot that is weakly coupled to the channel, i.e. when the connection of the channel to the dot transmits a single transport mode only. We explain this finding in terms of the Lippmann–Schwinger perturbation theory. We demonstrate that the signature of the weak coupling conditions is the conductance, which for P subbands at the Fermi level varies between and P in units of . For stronger coupling of the quantum dot to the channel, the G maps resolve the local density of states only for very specific work points, with the Fermi energy coinciding with quasi-bound energy levels.

Observable quasi-bound states of the H2 molecule

Characteristic parameters (energetic positions, widths, etc.) of the 23 spectroscopically observed (or potentially observable) quasi-bound energy levels for the ground state H(2) molecule are determined with high accuracy. The recent advances concerning nonadiabatic, relativistic, and quantum electrodynamical corrections have been taken into consideration. Theoretical approach is based on the careful investigation of the energy dependences of the real stationary scattering-state wave functions (their phase shifts and amplitudes). These energy dependences can be very accurately fitted to simple analytic formulas resulting from the quantum scattering theory. General criteria for the assignment of quasi-bound states are discussed and a new criterion is proposed, which excludes too broad and ambiguous resonances. To implement the proposed approach, a special high-precision computational method was used, which is described in full detail.

Observation of quasibound energy levels in the [MATH] state of 7 Li2

Double resonance excitation of 7 Li 2 vapour with two tunable single mode lasers (Ti-sapphire and R6G dye) have been used to study levels of the B 1 Π u state close to the potential maximum of this state (500±3 cm -1 above the dissociation limit). A potential energy curve has been constructed, and measured linewidths are consistent with those calculated from the potential energy curve

Resonant tunneling through a symmetric triple-barrier structure.

We consider tunneling of electrons through a triple-barrier structure. We focus our attention on the transmission coefficient T when the incident energy of the electrons is resonant with one of the quasibound energy levels of the structure. Although it is widely recognized that for a symmetric double-barrier structure T goes to unity at resonance, we shall show that this is not always the case for a symmetric triple-barrier structure in which the external barriers are half the width of the internal barrier.

Solving the Schrodinger equation in arbitrary quantum-well potential profiles using the transfer matrix method

A simple, accurate, and fast algorithm for solving the one-dimensional time-independent Schrodinger equation is presented. The algorithm is based on the transfer matrix method. This makes it possible to calculate all bound and quasi-bound energy levels and the corresponding wave functions for an arbitrarily shaped potential profile. The results of calculations are compared with those obtained by other authors for various types of problems. A central part of this study deals with solving the Schrodinger equation in quantum-well structures. The results show that the transfer matrix method is as accurate as other methods, but it is easier to implement and, hence, is superior for calculations on small computer, such as a PC. >

Linewidths of quantum well eigenstates with finite barriers

The linewidth of quasi-bound eigenstates in quantum wells is an important parameter in understanding interband absorption in quantum confined Stark effect modulators, intersubband absorption in quantum well infrared detectors, tunneling phenomena in resonant tunneling diodes, and transport in quantum well transistors. We investigate the linewidths for the quasi-bound energy levels of a quantum well with finite barrier height and width as the barrier width is varied. For a GaAs/Al xGa 1−xAs quantum well with a barrier height of 240 meV, well width of 80 Å, and barrier widths varying from 30 to 80 Å, we find a linewidth for the ground state that increases from 0.06 meV at barrier width of 60 Å to 2.03 meV at 30 Å; for the excited state, the linewidth is significantly larger, increasing from 0.49 meV for a barrier width of 80 Å to 21.71 meV at 30 Å. The ground eigenstate has a narrow linewidth, less than 0.2 meV, for barrier widths greater than 50 Å indicating the applicability of the quasi-bound approximation, whereas the excited state is broad at all barrier widths less than 80 Å signifying large errors in the use of the quasi-bound approximation. The linewidths of both the ground and excited states are shown to be directly proportional to the transmission coefficient as determined by the Wentzel-Kramers-Brillouin (WKB) approximation, justifying its use in linewidth analysis in the literature.

Density of states and linewidths of quantum wells with applied electric field

We calculate the density of states and corresponding linewidths for the quasi-bound energy levels of a quantum well including both barriers of finite height and width, and an applied electric field. For a GaAs/AlxGa1−xAs quantum well with a well width of 85 Å, barrier width of 50 Å, and barrier height of 240 meV, we find a field-induced linewidth for the excited state that increases from 2.9 meV at a field of 25 kV/cm to 9.5 meV at 150 kV/cm. This corresponds to a tunneling lifetime of 228 fs at 25 kV/cm decreasing to 69 fs at 150 kV/cm. The ground eigenstate has a narrow linewidth, less than 1 meV, up to a field of 150 kV/cm. The quasi-bound approximation is shown to be applicable to the ground state, but not for the excited state.

A simple iterative method for resonance calculation

A recently developed procedure for solving the stationary Schrodinger equation in matrix representation form is proved to be useful in calculating quasibound energy levels. Results for a simple quantum mechanical model with potential energy function V=-r-1+ lambda r( lambda <0) are shown to be very accurate.

Observation of the quasibound energy levels and tunnelling lifetimes in the Na 2 B 1Π u state

All quasibound vibrational energy levels υ′= 27–33 of the Na 2 B 1 Π u state are accessed via a triple resonance excitation scheme: cw modulated gain spectroscopy (MGS). Two independent analyses involve a Padé-type near-dissociation representation of the observed energies and non-linear least-squares fits to the lineshapes. The results are values for the barrier height (379.3 ±2.3 cm −1 above the center of gravity of the 3s + 3p separated atom limit), the total number of quasibound, rotationless energy levels (υ′max = 33), and tunnelling lifetimes for υ′= 33, J = 3–17 (τ = 93.5 ± 2.8 ps-18.3 ± 1.1 ps).

Calculation of bound and quasi-bound energy levels of the ground state of H g H: Matrix method

The bound and quasi-bound energy levels for theX 2Σ+ state of the H g H molecule were calculated by sing the matrix method in the harmonic-oscillator representation. The results are in very good agreement with the experimental ones.