China
Africa
Explore chapters and articles related to this topic
The Schrödinger equation
Published in David K Ferry, Quantum Mechanics, 2001
We can summarize these results by saying that for small amplitudes of the potential, or for small widths, there is at least one bound state lying just below the top of the well. As the potential, or width, increases, additional bound states become possible. The first (and, perhaps, only) bound state has an even-symmetry wave function. The next level that becomes bound will have odd symmetry. Then a second even-symmetry wave function will be allowed, then an odd-symmetry one, and so on. In the limit of an infinite potential well, there are an infinite number of bound states whose energies are given by (2.53).
Applications of the Formalism-I
Published in Shabnam Siddiqui, Quantum Mechanics, 2018
A particle inside a barrier that has high potential walls such that the particle's energy (E) is much less than the height of wall of potential. Such a particle will be stuck between the walls and will oscillate back and forth between the walls (turning points). This state of the particle is called a “bound state.”
Field-Free Dynamics
Published in Thomas C. Weinacht, Brett J. Pearson, Time-Resolved Spectroscopy, 2018
Thomas C. Weinacht, Brett J. Pearson
This could correspond to a “predissociative” potential, which does not support truly bound states since the barrier is finite. Such predissociative potentials can arise from the coupling between two diabatic potential energy surfaces (one bound and one dissociative).
Impurity-related optical response in a 2D and 3D quantum dot with Gaussian confinement under intense laser field
Published in Philosophical Magazine, 2020
H. Sari, E. Kasapoglu, S. Sakiroglu, I. Sökmen, C. A. Duque
In Figure 1(a), we present the first six confined electron energy levels in the 2DQD as a function of the effective 2DQD radius R. As is evident from the figure, due to the circular symmetry property of the system, some excited energy levels are two-fold degenerate. In addition, due to a reduction in electron confinement, the energy values decrease when the effective 2DQD radius R increases. Figure 1(b) depicts the energies of the electron bound to an on-centre hydrogenic donor impurity, as a function of the effective dot radius R. It should be noted that the degeneracy of the excited energy levels does not disappear because the Coulomb interaction potential is circularly symmetric. The impurity binding energies corresponding to the first four energy levels [, with i = 1,2,3,4, where and are the energy levels in Figure 1(a,b), respectively] are given in Figure 1(c). As can be seen from the curves of the binding energies, the carriers in the ground state are strongly bound to the hydrogenic impurity compared to those in the excited energy levels. Note that the binding energy curves in Figure 1(c) are plotted from the value of the radius for which each curve in Figure 1(a) corresponds to a bound state, that is, the energy of each state is below the height of the potential barrier- meV. The maximum observed in all the binding energy curves, for small values of the R-radius is due to the fact that under such conditions of the geometry the wave functions of the different states overflow into the material of the barrier and extend over the space losing the effects of the confinement of the heterostructure. It is clear that the more spatially extended the state under consideration, the greater the value of the R-radius for which the maxima appear, as seen in Figure 1(c). Finally, comparing the results obtained by the diagonalisation technique (solid lines) and FEM calculations (full symbols), we observe the excellent agreement between the two methods used to solve the differential equations involved in the study. We would like to emphasise that in the case of diagonalisation, the results have been tested with a convergence of up to 1.0 meV for at least the first ten states with the lowest energy.