The Schr\"odinger-Newton equation has frequently been studied as a nonlinear modification of the Schr\"odinger equation incorporating gravitational self-interaction. However, there is no evidence yet as to whether nature actually behaves this way. This work investigates a possible way to experimentally test gravitational self-interaction. The effect of self-gravity on the interference of massive particles is studied by numerically solving the Schr\"odinger-Newton equation for a particle passing through a double-slit. The results show that the presence of gravitational self-interaction has an effect on the fringe width of the interference that can be tested in matter-wave interferometry experiments. Notably, this approach can distinguish between gravitational self-interaction and environment-induced decoherence, as the latter does not affect the fringe width. This result will also provide a way to test if gravity requires to be quantized on the scale of ordinary quantum mechanics.The Schr\"odinger-Newton equation has frequently been studied as a nonlinear modification of the Schr\"odinger equation incorporating gravitational self-interaction. However, there is no evidence yet as to whether nature actually behaves this way. This work investigates a possible way to experimentally test gravitational self-interaction. The effect of self-gravity on the interference of massive particles is studied by numerically solving the Schr\"odinger-Newton equation for a particle passing through a double-slit. The results show that the presence of gravitational self-interaction has an effect on the fringe width of the interference that can be tested in matter-wave interferometry experiments. Notably, this approach can distinguish between gravitational self-interaction and environment-induced decoherence, as the latter does not affect the fringe width. This result will also provide a way to test if gravity requires to be quantized on the scale of ordinary quantum mechanics.

arXiv:2203.01787Physical Review AJul 21, 20222 citations

Remarks on Schrödinger's wave mechanics

Viktor Trkal

Časopis pro pěstování matematiky a fysikyJan 1, 19280 citations

The Schrödinger Equation and Negative Energies

Stanley A. Bruce

Abstract It is known that there is no room for anti-particles within the Schrödinger regime in quantum mechanics. In this article, we derive a (non-relativistic) Schrödinger-like wave equation for a spin- 1 / 2 $1/2$ free particle in 3 + 1 space-time dimensions, which includes both positive- and negative-energy eigenstates. We show that, under minimal interactions, this equation is invariant under 𝒫 𝒯 $\mathcal{P}\mathcal{T}$ and 𝒞 discrete symmetries. An immediate consequence of this is that the particle exhibits Zitterbewegung (‘trembling motion’), which arises from the interference of positive- and negative-energy wave function components.Abstract It is known that there is no room for anti-particles within the Schrödinger regime in quantum mechanics. In this article, we derive a (non-relativistic) Schrödinger-like wave equation for a spin- 1 / 2 $1/2$ free particle in 3 + 1 space-time dimensions, which includes both positive- and negative-energy eigenstates. We show that, under minimal interactions, this equation is invariant under 𝒫 𝒯 $\mathcal{P}\mathcal{T}$ and 𝒞 discrete symmetries. An immediate consequence of this is that the particle exhibits Zitterbewegung (‘trembling motion’), which arises from the interference of positive- and negative-energy wave function components.

Zeitschrift für Naturforschung ASep 19, 20182 citations

The Gauge Principle from the Schrodinger-Born Wave Mechanics

Pui Tak Leung

We propose an elementary way of introducing the gauge principle to beginners with a background in only mechanics, electromagnetism, and quantum mechanics. This evolves from an apparent conflict in the Schrodinger-Born formulation of wave mechanics, and does not have to resort to advanced concepts like covariant derivative and minimal coupling. With such an approach, one would have appreciated how interactions can be dictated from consideration of internal symmetry of a physical system, which serves as a principle underlying the foundation of almost all modern physics. In addition, the gauge principle also serves as a resource providing consistency between the Born rule and Schrodinger’s wave mechanics.We propose an elementary way of introducing the gauge principle to beginners with a background in only mechanics, electromagnetism, and quantum mechanics. This evolves from an apparent conflict in the Schrodinger-Born formulation of wave mechanics, and does not have to resort to advanced concepts like covariant derivative and minimal coupling. With such an approach, one would have appreciated how interactions can be dictated from consideration of internal symmetry of a physical system, which serves as a principle underlying the foundation of almost all modern physics. In addition, the gauge principle also serves as a resource providing consistency between the Born rule and Schrodinger’s wave mechanics.

Oct 31, 20200 citations

Schrödinger's Wave Mechanics

WORLD SCIENTIFIC eBooksMay 1, 20000 citations

1/2

free particle in 3 + 1 space-time dimensions, which includes both positive- and negative-energy eigenstates. We show that, under minimal interactions, this equation is invariant under 𝒫 𝒯

\mathcal{P}\mathcal{T}

and 𝒞 discrete symmetries. An immediate consequence of this is that the particle exhibits Zitterbewegung (‘trembling motion’), which arises from the interference of positive- and negative-energy wave function components.