  At present, there are many methods of quantum entanglement of particles with
an electromagnetic field. Most methods have a low probability of quantum
entanglement and not an exact theoretical apparatus based on an approximate
solution of the Schrodinger equation. There is a need for new methods for
obtaining quantum-entangled particles and mathematically accurate studies of
such methods. In this paper, a quantum harmonic oscillator (for example, an
electron in a magnetic field) interacting with a quantized electromagnetic
field is considered. Based on the exact solution of the Schrodinger equation
for this system, it is shown that for certain parameters there can be a large
quantum entanglement between the electron and the electromagnetic field.
Quantum entanglement is analyzed on the basis of a mathematically exact
expression for the Schmidt modes and the Von Neumann entropy.
