Maxwell coils are solenoids of spheroidal shape which produce a constant magnetic field inside the coil; at large distances the field of a Maxwell coil becomes that of a magnetic dipole. The current in systems consisting of several confocal Maxwell coils can be adjusted in such a way that the magnetic field inside the smallest coil is constant and the back flux is confined to the interior of the largest coil. Quantum-mechanical scattering of charged particles by Maxwell coils, or systems thereof, is first formulated as a three-dimensional problem and then treated within a two-dimensional approximation. The evolution in time of wave packets, which are Gaussian wave packets in the beginning, is calculated numerically. In all cases an Aharonov-Bohm effect is observed in the angular distribution of the scattered wave packets. The back flux results only in an additional deflection of the packets, which corresponds to the classical deflection caused by the Lorentz force.Maxwell coils are solenoids of spheroidal shape which produce a constant magnetic field inside the coil; at large distances the field of a Maxwell coil becomes that of a magnetic dipole. The current in systems consisting of several confocal Maxwell coils can be adjusted in such a way that the magnetic field inside the smallest coil is constant and the back flux is confined to the interior of the largest coil. Quantum-mechanical scattering of charged particles by Maxwell coils, or systems thereof, is first formulated as a three-dimensional problem and then treated within a two-dimensional approximation. The evolution in time of wave packets, which are Gaussian wave packets in the beginning, is calculated numerically. In all cases an Aharonov-Bohm effect is observed in the angular distribution of the scattered wave packets. The back flux results only in an additional deflection of the packets, which corresponds to the classical deflection caused by the Lorentz force.

Physical Review AMay 1, 19931 citation

Reduction of Wave Packet in Quantum Measurement

正也矢部

Jidō seigyo/Jido seigyoDec 10, 19930 citations

Neutron-multiwave-interference experiments with many resonance coils

Сергей Валентинович Григорьев, Yu. O. Chetverikov, A. V. Syromyatnikov +2 more

Neutron-multiwave-interference phenomena based on Ramsey's resonance method of ``separated oscillating fields'' are studied. A neutron passes through N successive resonant coils $(\ensuremath{\Elzxh}{\ensuremath{\omega}}_{0}=2{\ensuremath{\mu}}_{n}{B}_{0}),$ which flip the neutron spin with a probability $\ensuremath{\rho}$ smaller than 1. These coils are separated by path lengths L over which a homogeneous field ${B}_{1}$ is present. Because the spin-flip probability $\ensuremath{\rho}$ is smaller than 1, the number of waves for a neutron is doubled after each flipper, so as to produce ${2}^{N}$ neutron waves at the end of the setup. The phase difference between any pair of waves is a multiple of a ``phase quantum'' determined by the line integral of the field difference ${B}_{1}\ensuremath{-}{B}_{0}$ over the length L. Highly regular patterns of the quantum-mechanical probability R in ${(B}_{1},\ensuremath{\rho})$ space appear due to pair interference between individual waves. Possible applications of this phenomenon, such as a direct measurement of n-particle correlation function, are pointed out.Neutron-multiwave-interference phenomena based on Ramsey's resonance method of ``separated oscillating fields'' are studied. A neutron passes through N successive resonant coils $(\ensuremath{\Elzxh}{\ensuremath{\omega}}_{0}=2{\ensuremath{\mu}}_{n}{B}_{0}),$ which flip the neutron spin with a probability $\ensuremath{\rho}$ smaller than 1. These coils are separated by path lengths L over which a homogeneous field ${B}_{1}$ is present. Because the spin-flip probability $\ensuremath{\rho}$ is smaller than 1, the number of waves for a neutron is doubled after each flipper, so as to produce ${2}^{N}$ neutron waves at the end of the setup. The phase difference between any pair of waves is a multiple of a ``phase quantum'' determined by the line integral of the field difference ${B}_{1}\ensuremath{-}{B}_{0}$ over the length L. Highly regular patterns of the quantum-mechanical probability R in ${(B}_{1},\ensuremath{\rho})$ space appear due to pair interference between individual waves. Possible applications of this phenomenon, such as a direct measurement of n-particle correlation function, are pointed out.

Physical Review ASep 12, 20035 citations

The Quantum Mechanics of Trapped Wave Packets

Roy J. Glauber

Foundations of Quantum MechanicsApr 1, 19925 citations

{B}_{1}

is present. Because the spin-flip probability $\ensuremath{\rho}$ is smaller than 1, the number of waves for a neutron is doubled after each flipper, so as to produce

{2}^{N}

neutron waves at the end of the setup. The phase difference between any pair of waves is a multiple of a ``phase quantum'' determined by the line integral of the field difference ${B}_{1}\ensuremath{-}{B}_{0}$ over the length L. Highly regular patterns of the quantum-mechanical probability R in ${(B}_{1},\ensuremath{\rho})$ space appear due to pair interference between individual waves. Possible applications of this phenomenon, such as a direct measurement of n-particle correlation function, are pointed out.