UID:
almahu_9949199298302882
Format:
VII, 91 p. 1 illus.
,
online resource.
Edition:
1st ed. 1974.
ISBN:
9781475700343
Content:
1. Hilbert Space The words "Hilbert space" here will always denote what math ematicians call a separable Hilbert space. It is composed of vectors each with a denumerable infinity of coordinates ql' q2' Q3, .... Usually the coordinates are considered to be complex numbers and each vector has a squared length ~rIQrI2. This squared length must converge in order that the q's may specify a Hilbert vector. Let us express qr in terms of real and imaginary parts, qr = Xr + iYr' Then the squared length is l:.r(x; + y;). The x's and y's may be looked upon as the coordinates of a vector. It is again a Hilbert vector, but it is a real Hilbert vector, with only real coordinates. Thus a complex Hilbert vector uniquely determines a real Hilbert vector. The second vector has, at first sight, twice as many coordinates as the first one. But twice a denumerable in finity is again a denumerable infinity, so the second vector has the same number of coordinates as the first. Thus a complex Hilbert vector is not a more general kind of quantity than a real one.
Note:
1. Hilbert Space -- 2. Spinors -- Finite Number of Dimensions -- 3. Rotations in n Dimensions -- 4. Null Vectors and Null Planes -- 5. The Independence Theorem -- 6. Specification of a Null Plane without Its Coordinates -- 7. Matrix Notation -- 8. Expression of a Rotation in Terms of an Infinitesimal Rotation -- 9. Complex Rotations -- 10. The Noncommutative Algebra -- 11. Rotation Operators -- 12. Fixation of the Coefficients of Rotation Operators -- 13. The Ambiguity of Sign -- 14. Kets and Bras -- 15. Simple Kets -- Even Number of Dimensions -- 16. The Ket Matrix -- 17. The Two-Ket-Matrix Theorem -- 18. The Connection between Two Ket Matrices -- 19. The Representation of Kets -- 20. The Representative of a Simple Ket. General -- 21. The Representative of a Simple Ket. Special Cases -- 22. Fixation of the Coefficients of Simple Kets -- 23. The Scalar Product Formula -- Infinite Number of Dimensions -- 24. The Need for Bounded Matrices -- 25. The Infinite Ket Matrix -- 26. Passage from One Ket Matrix to Another -- 27. The Various Kinds of Ket Matrices -- 28. Failure of the Associative Law -- 29. The Fundamental Commutators -- 30. Boson Variables -- 31. Boson Emission and Absorption Operators -- 32. Infinite Determinants -- 33. Validity of the Scalar Product Formula -- 34. The Energy of a Boson -- 35. Physical Application.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9781475700367
Additional Edition:
Printed edition: ISBN 9781475700350
Additional Edition:
Printed edition: ISBN 9780306307980
Language:
English
DOI:
10.1007/978-1-4757-0034-3
URL:
https://doi.org/10.1007/978-1-4757-0034-3
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