A Course in mathematical physics / 4, Quantum mechanics of - download pdf or read online

By Walter E. Thirring

ISBN-10: 0387817018

ISBN-13: 9780387817019

ISBN-10: 3211817018

ISBN-13: 9783211817018

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Sample text

T; ZN /. 1), meaning that the particles are indistinguishable. 2/ because of the quadratic interaction imposed by the boundary condition. 3/ the equation for fN depends on fN . t; Zsout /. 4). 2). From now on we assume that fN decays at infinity in the velocity variable (the functional setting will be made precise in Chapter 5). t; Zsout/, we have Z RC R2dN @t fN C N X ! t; Zs /11ZN 2DN dZN using Green’s formula. 1, we may neglect configurations where more than two particles collide at the same time, so the boundary condition is well defined.

3). This construction, which is the technical part of the proof, will be detailed in Chapter 12. The conclusion of the convergence proof is presented in Chapters 13 and 14. 1). 3. sC1/ . sC1/ . t; Zs /d Vs ; 50 7 Strategy of the proof of convergence and they therefore involve infinite sums, as there may be infinitely many particles involved (the sum over n is unbounded). 2) and therefore to study the termwise convergence (for any fixed k), as expressed by the following statement. 1. Fix ˇ0 > 0 and 0 2 R.

Operations such as infinitesimal translations on the arguments require therefore a careful treatment. t; Zs / in terms of the initial data F0;N . 0/ Á 0 for j > N . ZsCk / Ä R2 ), and where the collision times are supposed to be well separated (namely, jtj tj C1 j ı). The reason for the two last assumptions is essentially technical, and will appear more clearly in the next step. The heart of the proof, in Part IV, is then to establish the termwise convergence, dealing with pathological trajectories.

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A Course in mathematical physics / 4, Quantum mechanics of large systems by Walter E. Thirring

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