By Edward G Harris

Written by means of a well known professor of physics, this introductory textual content is aimed at graduate scholars taking a year-long direction in quantum mechanics within which the 3rd area is dedicated to relativistic wave equations and box idea. tricky suggestions are brought progressively, and the speculation is utilized to bodily attention-grabbing problems.

After an introductory bankruptcy at the formation of quantum mechanics, the therapy advances to examinations of the quantum conception of the unfastened electromagnetic box, the interplay of radiation and topic, moment quantization, the interplay of quantized fields, and quantum electrodynamics. extra themes comprise the idea of beta decay, debris that have interaction between themselves, quasi debris in plasmas and metals, and the matter of infinities in quantum electrodynamics. The Appendix includes chosen solutions to difficulties that seem through the textual content.

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**Example text**

The term that remains when nbm= 0 . I s We consider spontaneous emission first. Stimulated emission may be treated together with absorption. . To f the excited state of an atom against spontaneous emission of a photon, we set n,, = 0 and sum Eq. 3-10 over all of the k's *and a's that the emitted photon can have. That is, Now we let the volume of the box in which the electromagnetic field is quantized become infinite. A very Problem 3-1. Prove Eq. 3-12. Hinr: use kd = 2mJL where n, is an integer to show that the number of states with k, in Ak-.

N,, + 1 . ) and n,, = 0,1,2,3, a(J- These relations are a consequence of Eq. 2-18. The state vectors of Eq. 2-23,are eigenvectors of Hrad with eigenvalues It may be shown that the momentum operator of the field, namely P ExB =//J' &-- is given by P = ):hkazga,, k,u Therefore the state vectors of Eq. 2-23 are also eigenvectors of P with eigenvalues On the basis of the preceding discussion it is natural to suppose that the electromagnetic field consist of photons each of which has the energy Aw, and momentum hk; ra,, is the number of photons with momentum 7% and polarization given by the vector u,,.

The amplitude of the wave is determined by the modulus of c and the phase is determined by the phase of c. This is the same form as Eq. 2-29 but the operators o and a+ have been replaced by the complex numbers c and cf. Brief caIcuIations like that of Eq. 2-36 show that Problem 2-1. Prove Eqs. 2-39a through 2-39c. We may define the uncertainty of the number of photons in the state Ic) in analogy with Eq. 1-67 by The relative uncertainty is This becomes very small when the expectation value of the number o f photons in this mode becomes very large.