Related papers: A new development of modified quantum mechanics
We propose a neural-network variational quantum algorithm to simulate the time evolution of quantum many-body systems. Based on a modified restricted Boltzmann machine (RBM) wavefunction ansatz, the proposed algorithm can be efficiently…
We study the general problem of mixing for ab-initio quantum-mechanical problems. Guided by general mathematical principles and the underlying physics, we propose a multisecant form of Broydens second method for solving the self-consistent…
Quantum friction, the electromagnetic fluctuation-induced frictional force decelerating an atom which moves past a macroscopic dielectric body, has so far eluded experimental evidence despite more than three decades of theoretical studies.…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…
Form factors of a simple system have been calculated in various forms of relativistic quantum mechanics, using a single-particle current. Their comparison has shown large discrepancies. The comparison is extended here to instant- and…
The complex-valued quantum mechanics considers quantum motion on the complex plane instead of on the real axis, and studies the variations of a particle complex position, momentum and energy along a complex trajectory. On the basis of…
A simple mapping procedure is presented by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed directly into those in curved space with torsion. Our procedure evolved from…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…
In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild-like metric. As a test, the hydrogen atom…
Action at distance in Newtonian physics is replaced by finite propagation speeds in classical post--Newtonian physics. As a result, the differential equations of motion in Newtonian physics are replaced by functional differential equations,…
The Schrodinger equation, Klein-Gordon equation (KGE), and Dirac equation are believed to be the fundamental equations of quantum mechanics. Schrodinger's equation has a defect in that there are no negative kinetic energy (NKE) solutions.…
Discussed is kinematics and dynamics of bodies with affine degrees of freedom, i.e., homogeneously deformable "gyroscopes". The special stress is laid on the status and physical justification of affine dynamical invariance. On the basis of…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum…
Quantum mechanics predicts a number of at first sight counterintuitive phenomena. It is therefore a question whether our intuition is the best way to find new experiments. Here we report the development of the computer algorithm Melvin…
In this educational paper, we will discuss calculations on the hydrogen molecule both on classical and quantum computers. In the former case, we will discuss the calculation of molecular integrals that can then be used to calculate…
With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.
Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories. While successful in nonrelativistic contexts, its extension to curved spacetime-and hence quantum…
Quantum computers promise to revolutionize our ability to simulate molecules, and cloud-based hardware is becoming increasingly accessible to a wide body of researchers. Algorithms such as Quantum Phase Estimation and the Variational…