Schrodinger Equation and (Future) Quantum Physics

акустика Механика

Rajan N. Iyer

This paper presents a novel and exact solution of the Schrödinger equation with zero potential energy, based on the analogy with Fick’s equation of diffusion. The author derived the wavefunction of a particle in a vacuum as an error function of the rotational phase angle, which corresponds to the geometry of a flat space. This solution reduces to the sinusoidal form of the wavefunction commonly used in quantum mechanics. The author also explored the implications of this solution for the connection between quantum physics and gas mechanics, and the possibility of using error functions and general transforms to model past, present, and future events in physics. The author used computer simulations to compare the error function solution and the sinusoidal solution in terms of response time, accuracy, and fit to the geometry of a flat space. The results showed that the error function solution was superior to the sinusoidal solution in all aspects, and that it had a stronger link to the gas mechanics, useful to Quantum ASTROPHYSICS. The results also suggested that the error function solution could be used to model past, present, and future events in physics, using error functions and general transforms. This paper is a preliminary analysis of the deeper physics underlying the error function solution of the Schrödinger equation, based on the author’s previous publications on point physics generalizing to Hod-PDP mechanism, field tensor modeling, string-metrics, and information-time event matrix formulations. The paper recommends that future research should extend the error function solution to space time geometry higher dimensions, non-zero potentials, and more diverse experiments. The paper also recommends that future research should explore the applications of error functions and general transforms within physics and other mathematical physical general related fields of sciences.

Chuanjin Zu, Xiangyang Yu

A significant obstacle impeding the advancement of the time fractional Schrödinger equation lies in the challenge of determining its precise mathematical formulation. In order to address this, we undertake an exploration of the time fractional Schrödinger equation within the context of a non-Markovian environment. By leveraging a two-level atom as an illustrative case, we find that the choice to raise i to the order of the time derivative is inappropriate. In contrast to the conventional approach used to depict the dynamic evolution of quantum states in a non-Markovian environment, the time fractional Schrödinger equation, when devoid of fractional-order operations on the imaginary unit i, emerges as a more intuitively comprehensible framework in physics and offers greater simplicity in computational aspects. Meanwhile, we also prove that it is meaningless to study the memory of time fractional Schrödinger equation with time derivative 1 < α ≤ 2. It should be noted that we have not yet constructed an open system that can be fully described by the time fractional Schrödinger equation. This will be the focus of future research. Our study might provide a new perspective on the role of time fractional Schrödinger equation.

Daniel R. Bes

Rostislav Stepanik

This QSTH 8.6.XS working publication proposes to read the Schrödinger equation as a ledger of coherent possibility rather than as a direct equation of finalized physical record formation. The publication does not claim that the Schrödinger equation is wrong, incomplete in its own domain, or superseded by QSTH. Instead, it asks a precise conceptual and methodological question: when does a coherent possibility acquire the right to become a stable record? Within the QSTH framework, the wave-function is interpreted as a structured ledger of possible evolution. Probability is not yet treated as completed reality, but as a pre-record layer of admissible possibility. The publication then introduces a careful distinction between standard quantum evolution, environmental decoherence, record formation, admissibility, and the later QSTH concept of Lambda_lock. The text also introduces a computationally cautious extension direction through a candidate locking functional, Gamma_lock. This is not presented as a derived physical law, but as a structured placeholder for future toy-models and numerical experiments describing the transition from possibility to record. A central contribution of this publication is the section Computability: what can already be modeled, which clarifies that several parts of the framework are already modelable as toy-models: standard Schrödinger evolution, non-Hermitian damping-like extensions, threshold locking integrals, and Hessian stability tests. Other QSTH layers remain candidates for future formalization. This publication belongs to the QSTH 8.x working sequence. It is not presented as a confirmed physical theory, but as a structured conceptual, mathematical, and methodological bridge toward QSTH 8.6.XP, QSTH 8.7, QSTH 8.12.H, and the later Equation of the Universe synthesis. Short description QSTH 8.6.XS reads the Schrödinger equation as a ledger of coherent possibility and asks when such possibility may acquire the right to become a stable record. It introduces Gamma_lock as a candidate functional and identifies which parts of the framework are already toy-model computable. Methodological status This publication is part of the QSTH CORE/CAND/SUPPORT/FUTURE framework. It should be read as a structured working publication, not as a confirmed physical model. Its purpose is to clarify the conceptual role of the Schrödinger equation as a ledger of possibility and to open a cautious computational bridge toward admissibility, Lambda_lock, record formation, and settlement stability. Computability note Several parts of the proposed framework are already computable as toy-models. Standard Schrödinger evolution can be simulated directly. A candidate non-Hermitian QSTH locking term can be explored by selecting provisional forms of Gamma_lock. Threshold conditions of the form integral Gamma_lock dt >= Lambda_lock can be numerically tested. Hessian stability can also be modeled once a candidate lock-potential or settlement landscape is defined. These are not yet confirmed physical laws. They are structured modeling entry points for future numerical testing, falsification, and comparison with null models. This record belongs to the QSTH 8.x publication sequence. It follows QSTH 8.6 — O-Dim and 0D Root Publication and acts as the Schrödinger-side companion branch of that root framework. QSTH 8.6.XS studies the transition from coherent possibility toward admissible record formation. It prepares later work on QSTH 8.6.XP, Lambda_lock, objective settlement, Hessian stability, spin-locking, and the Equation of the Universe synthesis. The publication includes a computability section intended as an open invitation for future toy-model construction, numerical testing, falsification, and scientific collaboration. QSTH 8.6.XS does not replace Schrödinger. It places a question beside him: when does the ledger of possibility acquire the right to become a ledger of record?