O Space Quantization in Time Varying Magnetic Fields.

The transitions between states of different space quantization which take place when an atom is passed through a weak inhomogeneous magnetic field are calculated by approximate methods taking into account the coupling between the nucleus and the orbital electrons. Two types of field are considered, namely, the field introduced by Majorana and the one introduced by G\"uttinger. For the Majorana field a discussion of the cases $I$ arbitrary $J=\frac{1}{2}$ , $J$ arbitrary $I=\frac{1}{2}$ , and $I$ and $J$ arbitrary with explicit application to the nitrogen atom is given. For the G\"uttinger field the general equations are set up for a field of any strength and are then applied to the case $I=J=\frac{1}{2}$ .The transitions between states of different space quantization which take place when an atom is passed through a weak inhomogeneous magnetic field are calculated by approximate methods taking into account the coupling between the nucleus and the orbital electrons. Two types of field are considered, namely, the field introduced by Majorana and the one introduced by G\"uttinger. For the Majorana field a discussion of the cases $I$ arbitrary $J=\frac{1}{2}$, $J$ arbitrary $I=\frac{1}{2}$, and $I$ and $J$ arbitrary with explicit application to the nitrogen atom is given. For the G\"uttinger field the general equations are set up for a field of any strength and are then applied to the case $I=J=\frac{1}{2}$.

Physical ReviewAug 15, 193616 citations

Quantum Time

Ashmead, John

Normally we quantize along the space dimensions but treat time classically. But from relativity we expect a high level of symmetry between time and space. What happens if we quantize time using the same rules we use to quantize space? To do this, we generalize the paths in the Feynman path integral to include paths that vary in time as well as in space. We use Morlet wavelet decomposition to ensure convergence and normalization of the path integrals. We derive the Schrödinger equation in four dimensions from the short time limit of the path integral expression. We verify that we recover standard quantum theory in the non-relativistic, semi-classical, and long time limits. Quantum time is an experiment factory: most foundational experiments in quantum mechanics can be modified in a way that makes them tests of quantum time. We look at single and double slits in time, scattering by time-varying electric and magnetic fields, and the Aharonov-Bohm effect in time.Normally we quantize along the space dimensions but treat time classically. But from relativity we expect a high level of symmetry between time and space. What happens if we quantize time using the same rules we use to quantize space? To do this, we generalize the paths in the Feynman path integral to include paths that vary in time as well as in space. We use Morlet wavelet decomposition to ensure convergence and normalization of the path integrals. We derive the Schrödinger equation in four dimensions from the short time limit of the path integral expression. We verify that we recover standard quantum theory in the non-relativistic, semi-classical, and long time limits. Quantum time is an experiment factory: most foundational experiments in quantum mechanics can be modified in a way that makes them tests of quantum time. We look at single and double slits in time, scattering by time-varying electric and magnetic fields, and the Aharonov-Bohm effect in time.

arXiv:1005.0789May 5, 20101 citation

Electromagnetic Field Quantization

Pierre Meystre

Graduate texts in physicsJan 1, 20210 citations

A hybrid approach for quantizing complicated motion of a charged particle in time-varying magnetic field

Salah Menouar, Jeong Ryeol Choi

Annals of PhysicsDec 6, 201413 citations

Magnetic fields and Bohr’s quantization rule

Subhash N. Karbelkar

ResonanceOct 1, 20130 citations

I

arbitrary

J=\frac{1}{2}

J

arbitrary

I=\frac{1}{2}

, and

I

and

J

arbitrary with explicit application to the nitrogen atom is given. For the G\"uttinger field the general equations are set up for a field of any strength and are then applied to the case

I=J=\frac{1}{2}