Related papers: Delay Time in Quaternionic Quantum Mechanics
A formulation of quaternionic quantum mechanics ($\mathbb{H}$QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After…
Inside quantum mechanics the problem of decoherence for an isolated, finite system is linked to a coarse-grained description of its dynamics.
A novel quantum time dilation effect is shown to arise when a clock moves in a quantum superposition of two relativistic velocities. This effect is argued to be measurable using existing atomic interferometry techniques, potentially…
Quantum time dilation occurs when a clock moves in a superposition of relativistic momentum wave packets. We utilize the lifetime of an excited hydrogen-like atom as a clock to demonstrate how quantum time dilation manifests in a…
We discuss the Schrodinger equation in presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to…
In this paper we present a perturbation theory for constant quaternionic potentials. The effects of quaternionic perturbations are explicitly treated for bound states of hydrogen atom, infinite potential well and harmonic oscillator.…
In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an…
Quantum particles interacting with potential barriers are ubiquitous in physics, and the question of how much time they spend inside classically forbidden regions has attracted interest for many decades. Recent developments of new…
Previously we presented general formulation of hidden time concept as a basis for building a dynamical picture underlying quantum mechanics. Here, we present detailed explanation of how hidden time works for basic quantum optical…
Tunneling delay times of wavepackets in quantum mechanical penetration of rectangular barriers have long been known to show a perplexing independence with respect to the width of the barrier. This also has relevence to the transmission of…
While in general there is no one-to-one correspondence between complex and quaternion quantum mechanics (QQM), there exists at least one version of QQM in which a {\em partial} set of {\em translations} may be made. We define these…
Delay times in quantum mechanics always represented an intriguing challenge for physicists. Due to the fact that quantum mechanical experiments are, often, hard to be implemented, the possibility to connect delay times with laser lateral…
We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex to quaternions, the calculation of the real-valued parameters of the CKM matrix drastically changes. We aim to explain this…
We examine how time ordering works in quantum mechanics and in classical mechanics.
The a priori time in conventional quantum mechanics is shown to contradict the uncertainty principle. A possible solution is given.
Time dilation is a difference in measured time between two clocks that either move with different velocities or experience different gravitational potentials. Both of these effects stem from the theory of relativity and are usually…
We propose a general construction of an observable measuring the time of occurence of an effect in quantum theory. Time delay in potential scattering is computed as a straightforward application.
We study the bound-state solutions of vanishing angular momentum in a quaternionic spherical square-well potential of finite depth. As in the standard quantum mechanics, such solutions occur for discrete values of energies. At first glance,…
A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special…
We study the statistical properties of the time delay matrix $Q$ in the context of quantum transport through a chaotic cavity, in the absence of time-reversal invariance. First, we approach the problem from the point of view of random…