Search results for "wave function"
showing 10 items of 395 documents
Energy levels of a quantum ring in a lateral electric field
2002
Abstract The electronic states of a semiconductor quantum ring (QR) under an applied lateral electric field are theoretically investigated and compared with those of a quantum disk of the same size. The eigenstates and eigenvalues of the Hamiltonian are obtained from a direct matrix diagonalization scheme. Numerical calculations are performed for a hard-wall confinement potential and the electronic states are obtained as a function of the electric field and the ratio r2/r1, where r2 (r1) is the outer (inner) radius of the ring. The effects of decreasing symmetry and mixing on the energy levels and wave functions due to the applied electric field are also studied. The direct optical absorpti…
NaK Λ doubling and permanent electric dipoles in low-lying1Πstates: Experiment and theory
1998
The paper presents \ensuremath{\Lambda} splittings and q factors in the NaK $D{}^{1}\ensuremath{\Pi}$ state, directly measured from the electric radio-frequency-optical double resonance (RF-ODR) in laser-induced fluorescence (LIF) for a number of vibrational states $v=1--22$ with definite rotational levels J between 7 and 46. Permanent electric dipole moment values (d) have been obtained by measuring in LIF spectra the relative intensities of ``forbidden'' lines caused by dc Stark effect induced $e/f$ mixing in the ${}^{1}\ensuremath{\Pi}$ state, with their subsequent processing, which allowed us to obtain the $q/d$ ratio. A possible influence of the hyperfine structure on the RF-ODR signal…
One-particle Green's function
2013
In this chapter we get acquainted with the one-particle Green's function G , or simply the Green's function. The chapter is divided in three parts. In the first part (Section 6.1) we illustrate what kind of physical information can be extracted from the different Keldysh components of G . The aim of this first part is to introduce some general concepts without being too formal. In the second part (Section 6.2) we calculate the noninteracting Green's function. Finally in the third part (Sections 6.3 and 6.4) we consider the interacting Green's function and derive several exact properties. We also discuss other physical (and measurable) quantities that can be calculated from G and that are re…
Coulomb Fourier Transformation: Application to a Three-Body Hamiltonian with One Attractive Coulomb Interaction
2003
Consider a three-body system consisting of one neutral particle 1 and two charged particles characterized by the indices 2 and 3 with charges of opposite sign, i.e., e2e3 < 0. We use the following notation: (x ν , y ν ), v = 1, 2, 3, denotes the (mass-renormalized) coordinate vector within the pair ν, and between the center of mass of the pair ν and particle ν, respectively. The corresponding canonically coniugate momenta are (k ν , p ν ).
Multifractal Properties of Eigenstates in Weakly Disordered Two-Dimensional Systems without Magnetic Field
1992
In order to investigate the electronic states in weakly disordered 2D samples very large (up to 180 000 * 180 000) secular matrices corresponding to the Anderson Hamiltonian are diagonalized. The analysis of the resulting wave functions shows multifractal fluctuations on all length scales in the considered systems. The set of generalized (fractal) dimensions and the singularity spectrum of the fractal measure are determined in order to completely characterize the eigenfunctions.
Beyond the Runge–Gross Theorem
2012
The Runge–Gross theorem (Runge and Gross, Phys Rev Lett, 52:997–1000, 1984) states that for a given initial state the time-dependent density is a unique functional of the external potential. Let us elaborate a bit further on this point. Suppose we could solve the time-dependent Schrodinger equation for a given many-body system, i.e. we specify an initial state \(| \Uppsi_0 \rangle\) at \(t=t_0\) and evolve the wavefunction in time using the Hamiltonian \({\hat{H}} (t).\) Then, from the wave function, we can calculate the time-dependent density \(n (\user2{r},t).\) We can then ask the question whether exactly the same density \(n(\user2{r},t)\) can be reproduced by an external potential \(v^…
On Scattering and Bound States for a Singular Potential
1970
To understand the origin of the difficulties in the determination of the physical wavefunc tion for an attractive inverse square potential, we study a model in which the singularity at the origin is substituted by a repulsive core. The structure of the spectrum of energy levels is discussed in some detail. The physical interpretation of the solutions of the Schrodinger equation for a potential of the form - (-h 2 /2m) 11/ r 2 presents difficulties, which occur for 11 larger than (l + 1/2)\ where l is the angular momentum. The difficulties are due to the fact that the condition of square integrability usually imposed on the wavefunction is not sufficient in this case to determine phase shif…
The Pauli Principle and Systems Consisting of Composite Particles
1993
In nature we often deal with many-body systems that are described in terms of particles that are not elementary but themselves composite. Examples of such composite particles are hadrons, atoms, phonons, and Cooper pairs. For the description of systems consisting of such composite particles in terms of the underlying degrees of freedom group theory plays an important role, in particular the symmetric group to describe the permutational symmetry of the wave function of the system, and unitary groups to describe the symmetry forced on the system by the interaction between the particles.
Electronic structure of a quantum ring in a lateral electric field
2001
The electronic states of novel semiconductor quantum rings (QR's) under applied lateral electric fields are theoretically investigated for different values of the ratio ${r}_{2}{/r}_{1},$ where ${r}_{2}$ ${(r}_{1})$ is the outer (inner) radius of the ring. The eigenstates and eigenvalues of the Hamiltonian are obtained from a direct matrix diagonalization scheme. Numerical calculations are performed for a hard-wall confinement potential and the electronic states are obtained as a function of the electric field and the ratio ${r}_{2}{/r}_{1}.$ An anomalous behavior in the energy vs. electric-field fan plot due to the break of symmetry is predicted. Analytical expressions for the energy level…
Computation of conical intersections by using perturbation techniques
2005
Multiconfigurational second-order perturbation theory, both in its single-state multiconfigurational second-order perturbation theory (CASPT2) and multistate (MS-CASPT2) formulations, is used to search for minima on the crossing seams between different potential energy hypersurfaces of electronic states in several molecular systems. The performance of the procedures is tested and discussed, focusing on the problem of the nonorthogonality of the single-state perturbative solutions. In different cases the obtained structures and energy differences are compared with available complete active space self-consistent field and multireference configuration interaction solutions. Calculations on dif…