I reply to Finkelstein’s comment [preceding paper, Phys. Rev. A 60, 1723 (1999)] and remark on the meanings conveyed by the word “amplitude.”

In a recent paper Robicheaux and Shaw [Phys. Rev. A 58, 1043 (1998)] calculated the recurrence spectra of atoms in electric fields with nonvanishing angular momentum $〈L_z〉\ne 0$. Features are observed at scaled actions “an order of magnitude shorter than for any classical closed orbit of this system.” We investigate the transition from zero to nonzero angular momentum and demonstrate the existence of short closed orbits with $L_z\ne 0$. The real and complex “ghost” orbits are created in bifurcations of the “uphill” and “downhill” orbit along the electric-field axis, and can serve to interpret the observed features in the quantum recurrence spectra.

We discuss some of the difficulties in using the orbits proposed by Main [preceding paper, Phys. Rev. A 60, 1726 (1999)] to calculate the recurrence spectra in Robicheaux and Shaw [Phys. Rev. A 58, 1043 (1998)].

Analytical solutions and fresh insights for the relativistic dynamics of charges in classical electromagnetic fields are made possible by an eigenspinor approach. The Lorentz-force equation takes a simple spinorial form when expressed in terms of an amplitude of the Lorentz transformation that describes the motion of the charge in Clifford’s geometric algebra of physical space. Algebraic projectors allow explicit analytical solutions to be found for charges in arbitrary initial motion interacting with monochromatic plane waves, with directed plane-wave pulses, and with pulses superimposed on static axial fields. The treatment tests the classical effective mass of a dressed charge and leads to a refinement of the concept of ponderomotive momentum. Implications for a pulsed autoresonance laser accelerator are briefly discussed.

We consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe that both our model Hamiltonian and its supersymmetric partner may have normalizable zero-energy ground states, in contrast to local models with nonperiodic or periodic potentials.

We present a detailed description of a procedure for the numerical evaluation of the first-order self-energy correction for an arbitrary excited state. An efficient schema of the numerical treatment of the many-potential part of the Dirac-Coulomb Green function improves the speed of the computation considerably. This feature is extremely important for higher-order self-energy calculations. We apply this method to the evaluation of the self-energy correction for the excited states with $|\kappa |<~5$ and $n<~5$ for some high-$Z$ ions.

We define Sturmian basis functions for the harmonic oscillator, and investigate whether recent insights into Sturmians for Coulomb-like potentials can be extended to this important potential. We also treat many-body problems such as coupling to a bath of harmonic oscillators. Comments on coupled oscillators and time-dependent potentials are also made. It is argued that the Sturmian method amounts to a nonperturbative calculation of the energy levels, but the limitations of the method is also pointed out, and the cause of this limitation is found to be related to the divergence of the potential. Thus the divergent nature of the anharmonic potential leads to the Sturmian method being less accurate than in the Coulomb case. We discuss how modified anharmonic oscillator potentials, which are well behaved at infinity, leads to a rapidly converging Sturmian approximation.

We define a new measurement of entanglement, the entanglement of projection, and find that it is natural to write the entanglements of formation and assistance in terms of it. Our measure allows us to describe a new class of quantum erasers which restore entanglement rather than just interference. Such erasers can be implemented with simple quantum computer components. We propose realistic optical versions of these erasers.

We investigate tunneling through a barrier and reflection over a step potential in the limit of long waves, i.e., near the base of the barrier, or for barriers with a small action integral over the forbidden region, and at the top of the ramp where the usual semiclassical approximation breaks down systematically. General approximations of the probability of transmission and reflection are given and compared to competing ones showing that the present approach based on the comparison method can give far better results.

The dynamics of systems composed of a classical sector plus a quantum sector is studied. We show that, even in the simplest cases, (i) the existence of a consistent canonical description for such mixed systems is incompatible with very basic requirements related to the time evolution of the two sectors when they are decoupled, (ii) the classical sector cannot inherit quantum fluctuations from the quantum sector, and (iii) a coupling among the two sectors is incompatible with the requirement of physical positivity of the theory, i.e., there would be positive observables with a nonpositive expectation value.

The classical deflection function for scattering by a radially symmetric potential corresponds to twice the angular momentum derivative of the scattering phase shifts calculated in the conventional WKB approximation. A “quantum-mechanical deflection function” defined as twice the angular momentum derivative of the quantum-mechanical phase shifts (without WKB approximation) is able to incorporate into the simple trajectory picture certain quantum aspects of the scattering process, e.g., the influence of the Goos-Hänchen shift. We demonstrate the performance of this quantum-mechanical deflection function for sharp-edged and smooth-edged two-dimensional scattering potentials.

A quantum theory that applies to the (closed) universe needs to be time asymmetric because of the cosmological arrow of time. The preparation $\Rightarrow$ registration arrow of time (a state must be prepared before an observable can be detected in it) of the quantum mechanics of measured systems provides a phenomenological reason for an asymmetric semigroup time evolution. The standard theory in the Hilbert space (HS) is inadequate for either since the mathematics of the HS allows only reversible unitary group evolution and time symmetric boundary conditions. The mathematical theory that describes time-asymmetric quantum physics in addition to providing the mathematics for the Dirac kets is the rigged Hilbert space (RHS) theory. It uses a pair of RHS’s of Hardy class with complementary analyticity property, one for the prepared states (“in states”) and the other for the registered observables (“out states”). The RHS’s contain Gamow kets which have all the properties needed to represent decaying states and resonances. Gamow kets have only asymmetric time evolution. The neutral kaon system is used to show that quasistationary microphysical systems can be experimentally isolated if their time of preparation can be accurately identified. The theoretical predictions for a Gamow ket have the same features as the observed decay probabilities, including the time ordering. This time ordering is the same as the time ordering in the probabilities of histories for the quantum universe. The fundamental quantum mechanical arrow of time represented by the semigroup in the RHS is therefore the same as the cosmological arrow of time, assuming that the universe can be considered a closed quantum system.

Two proofs are presented which show that quantum mechanics is incompatible with the following assumption: all possible correlations between subsystems of an individual isolated composite quantum system are contained in the initial quantum state of the whole system, although just a subset of them is revealed by the actual experiment.

We study the physical quantum resources required to implement general quantum operations, and provide bounds on the minimum possible size which an environment must be in order to perform certain quantum operations. We prove that contrary to a previous conjecture, not all quantum operations on a single qubit can be implemented with a single-qubit environment, even if that environment is initially prepared in a mixed state. We show that a mixed single-qutrit environment is sufficient to implement a special class of operations, the generalized depolarizing channels.

The quantum radiation field inside a double cavity is examined. The double cavity consists of a cavity containing a reflecting mirror. Two independent radiation fields are present inside the cavity. It is then assumed that the mirror becomes suddenly transparent. The double cavity transforms thus into a single cavity. The relationship between the radiation fields before and after the change is investigated. It is shown that the sudden change excites the radiation modes of the single cavity. Only modes having a node at the position of the mirror are not excited. The sudden change of the mirror’s reflectivity can thus generate photons from the vacuum. It is also shown that the sudden change produces squeezing. These features of the double cavity are then employed in a gedankenexperiment for the generation of entanglement between noninteracting atoms with the quantum eraser technique.

We analyze properties of the quantum conditional amplitude operator [Phys. Rev. Lett. 79, 5194 (1997)], which plays a role similar to that of the conditional probability in classical information theory. The spectrum of the conditional operator that characterizes a quantum bipartite system is shown to be invariant under local unitary transformations and reflects its inseparability. More specifically, it is proven that the conditional amplitude operator of a separable state cannot have an eigenvalue exceeding 1, which results in a necessary condition for separability. A related separability criterion based on the non-negativity of the von Neumann conditional entropy is also exhibited.