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We will quantize the Hamiltonian. Note that quantum momentum operator will now include momentum in the field, not just the particle's momentum. As this Hamiltonian is written, is the variable conjugate to and is related to the velocity by. The computation yields. The Zeeman effectneglecting electron spin, is particularly simple to calculate because the the hydrogen energy eigenstates are also eigenstates of the additional term in the Hamiltonian.
Hence, the correction can be calculated exactly and easily. The additional magnetic field terms are important in a plasma because the typical radii can be much bigger than in an atom. A plasma is composed of ions and electrons, together to make a usually quantum neutral mix.
The charged particles are essentially free to move in the plasma. If we apply an external magnetic field, we have a quantum mechanics read more to solve. On earth, we use plasmas in magnetic fields for many things, including nuclear fusion reactors.
Most regions of space hamiltonian plasmas and magnetic fields. In the example quantum, we will solve the Quantum Mechanics problem two ways: one using our new Hamiltonian with B field terms, and the other writing the Hamiltonian in terms of A.
The first one hamiktonian exploit both rotational symmetry about hamiltonian B field direction and translational hamiltonian hamlitonian the B field direction.
We will turn the radial equation into the equation we solved for Hydrogen. In the second solution, we will use translational symmetry along the B hamiltonoan direction as well as translational symmetry transverse to the B field.
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