Related papers: Critical Missing Equation of Quantum Physics for U…
We study a quantum theory based on two assumptions: In the intrinsic frame of reference of an isolated, macroscopic system, (i) the system has no global motion and is not entangled with any other system, (ii) time evolution of statevectors…
It is shown that in one-particle Schr\"{o}dinger quantum mechanics a small perturbation of a one-dimensional potential can produce a large change in the ground state, the effect becoming more pronounced with growing typical length of the…
Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a…
In classical mechanics the local exponential instability effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. We…
The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schr\"odinger cat state,…
It is shown that the time-dependent equations (Schr\"odinger and Dirac) for a quantum system can be always derived from the time-independent equation for the larger object of the system interacting with its environment, in the limit that…
By assuming that the kinetic energy,potential energy,momentum,and some other physical quantities of a particle exist in the field out of the particle,the Schrodinger equation is an equation describing field of a particle,but not the…
A quantum phase transition may occur in a system at zero temperature when a controlling parameter is tuned towards a critical point. An important question is whether such a critical point exists in a particular system and how stable it is.…
The study of quantum systems evolving from initial states to distinguishable, orthogonal final states is important for information processing applications such as quantum computing and quantum metrology. However, for most unitary evolutions…
Here I show that a classical or quantum bit state plus one simple operation, an action, are sufficient ingredients to derive a quantum dynamical equation that rules the sequential changes of the state. Then, by assuming that a freely moving…
The internal structure of self-interacting quantum particle like electron is independent on space-time position. Then at least infinitesimal kinematic space-time shift, rotation or boost lead to the equivalent internal quantum state. This…
The Schr\"odinger equation in high dimensions describes the evolution of a quantum system. Assume that we are given the evolution map sending each initial state $f\in L^2(\mathbb{R}^n)$ of the system to the corresponding final state at a…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
The Schr\"{o}dinger equation admits smooth and finite solutions that spontaneously evolve into a singularity, even for a free particle. This blowup is generally ascribed to the intrinsic dispersive character of the associated time…
The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the quantization of the Noether momenta. These can be…
The dynamical equation of hybrid systems, being the combination of Schr\"odinger and Liouville equations, produces noncausal evolution when the initial state of interacting quantum and classical mechanical systems is as it is demanded in…
Phase transitions which occur at zero temperature when some non-thermal parameter like pressure, chemical composition or magnetic field is changed are called quantum phase transitions. They are caused by quantum fluctuations which are a…
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…
By solving the Schr\"odinger equation one obtains the whole energy spectrum, both the bound and the continuum states. If the Hamiltonian depends on a set of parameters, these could be tuned to a transition from bound to continuum states.…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…