Fock's Theory: Quantum Coulomb Problem

Fock's theory is fundamental to which atomic element?

Fock's theory allows realization of the rotation group of a 3D sphere in what space?

What type of space is used to simplify the Schrödinger equation in the modified Fock's theory?

In modifying Fock's theory, invariant tensor methods of electrostatics are used in which spaces?

In the modified Fock's theory, which equation does the Schrödinger equation become in a 4D coordinate space?

In the modified Fock's theory, the transition from harmonic 4D polynomials to the original 3D physical space involves derivatives with respect to which entity?

The Schwinger resolvent can be derived by what method?

What is the quantum Coulomb problem fundamental for calculating?

The group SO(4) of rotations in four dimensional space represents an underlying symmetry of what?

In quantum mechanics, what do the classical vector integrals correspond to?

The transformation of variables and operators maps the original quantum Coulomb problem into another problem, what is it?

In Fock's approach, what is the starting point in his theory?

What is applied in this paper to eigenfunctions extended harmonically to the 4D momentum space?

What are the eigenfunctions when transitioning to the 4D coordinate space in the modified Fock's theory?

The advantage of using tensors in the perturbation theory is demonstrated in calculating which effect?

To modify the Fock theory, what is convenient to use in moving to the 4D coordinate space?

When harmonic tensors are used, what coordinate is singled out in the physical space?

What gets multiplied by the imaginary unit i and equated to the length of the radius vector |r|?

What remains unchanged under transformations when using harmonic tensors?

The extension from the Fock sphere into 4D space is linked to the use of what mathematical objects?

The state correspondence found in this paper is generated by physical symmetry of the problem and is not known in theory of what mathematical entities?

In the momentum representation, what argument do the eigenfunctions of the Schrödinger equation have?

Applying the Laplace operator to P(x) results in what?

The rules for using what are demonstrated in Section 3 of the article?

For the dipole state, the solution is expressed as what?

In Fock's theory, the first step involves multiplying the function $a_{nl}(p)$ by what?

Which projection doubles the tilt angle φ?

In the new variables, with Fock's factor, what becomes the eigenfunction?

When the potential of a point charge is expanded in powers of coordinates $x_{0i}$ what arises?

A contraction over any two indices results in zero, what conditions are required for this?

When calculating a multipole potential, what can be used instead of spherical functions?

What is the last equality called in the expression $AP(x) = 0, P(cx) = c'P(x), (xV)P(x) = lP(x)$?

When does the electric field have discontinuity 4πσ?

How is the potential of a point charge expressed in 4D space?

The harmonic tensor in nominator has a structure similar to which equation?

The electric polarizability is $9a_0^3 / 2$. Under what condition is this true?

The first modification of Fock's theory is the transition from where to where?

According to Eq. (79), functions are inverted with respect to which geometrical object?