A new proof of existence of a bound state in the quantum Coulomb field. II. (English) Zbl 1204.81092
Summary: The wave function of the bound state of the quantum Coulomb field is explicitly constructed. We define a sequence of obviously legal states in the Hilbert space of the quantum theory of the Coulomb field and show that for \(0 < e^2/\pi\hbar c < 1\) this sequence does have the Cauchy property while for \(e^2/\pi\hbar c > 1\) it does not have this property. The average value of the first Casimir operator \(C_1 = -(\frac12) M_{\mu\nu}M^{\mu\nu}\) is shown to converge to the previously calculated eigenvalue \(z(2-z)\), \(0 < z = e^2/\pi\hbar c < 1\).
Parts I and III, Acta Phys. Pol. B 35, 2249–2260 (2004), and ibid. 40, No. 12, 3771– 3775 (2009).
Parts I and III, Acta Phys. Pol. B 35, 2249–2260 (2004), and ibid. 40, No. 12, 3771– 3775 (2009).
MSC:
81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
81V10 | Electromagnetic interaction; quantum electrodynamics |
Keywords:
fine structure constantReferences:
[1] | Dirac, P. A.M., Int. J. Theor. Phys., 23, 677-681 (1984) |
[2] | Dirac, P. A.M., (The Principles of Quantum Mechanics (1947), Cambridge University Press), 304 · Zbl 0030.04801 |
[3] | Staruszkiewicz, A., Ann. Phys. (NY), 190, 354-372 (1989) |
[4] | Staruszkiewicz, A., Acta Phys. Pol. B, 35, 2249-2259 (2004) |
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