On the Eigenfunctions of Many Particle Systems in Quantum Mechanics
On the Eigenfunctions of Many Particle Systems in Quantum Mechanics
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In our eReader you can find the full English version of the book. Read On the Eigenfunctions of Many Particle Systems in Quantum Mechanics Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book On the Eigenfunctions of Many Particle Systems in Quantum Mechanics
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The operators G V. Are somewhat more complicated. According to the definition of the product of two operators in a Hilbert space, G7. Is defined - 22 - only for functions u such that V. U and G(7. U) are both defined. But the V. Are in general unbounded and not defined everywhere, and hence the GV. Are also not defined everjrwhere. It can be shown, however, that the G7, are never- theless bounded.
In what follows let V stand for any one of the V. For simplicity. Then the operator OV is obviousl...y a restriction of the integral operator A defined by (U. L) (Au) (x) - I g(x-y) V(y) u(y) dy, and, as we shall show, A is a bounded linear operator defined everywhere in ^ ♦ More generally, we can regard A as a linear operator which transforms an element from a Banach space L^ ■» L^(E ) into another Banach space L^, Here m L^ is, as usual, the space of all (equivalent classes of) complex-valued functions u(x) with the finite p-nonn 1/p (U. 2) Hull r!u(x)|Pdx We shall consider the values 2 § p $ oo and define as usual Iju ||^" sup|u(x)|, Ap a linear operator on L^ to L*', Au is defined for u e.
What to read after On the Eigenfunctions of Many Particle Systems in Quantum Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by Tosio Kato to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The operators G V. Are somewhat more complicated. According to the definition of the product of two operators in a Hilbert space, G7. Is defined - 22 - only for functions u such that V. U and G(7. U) are both defined. But the V. Are in general unbounded and not defined everywhere, and hence the GV. Are also not defined everjrwhere. It can be shown, however, that the G7, are never- theless bounded.
In what follows let V stand for any one of the V. For simplicity. Then the operator OV is obviousl...y a restriction of the integral operator A defined by (U. L) (Au) (x) - I g(x-y) V(y) u(y) dy, and, as we shall show, A is a bounded linear operator defined everywhere in ^ ♦ More generally, we can regard A as a linear operator which transforms an element from a Banach space L^ ■» L^(E ) into another Banach space L^, Here m L^ is, as usual, the space of all (equivalent classes of) complex-valued functions u(x) with the finite p-nonn 1/p (U. 2) Hull r!u(x)|Pdx We shall consider the values 2 § p $ oo and define as usual Iju ||^" sup|u(x)|, Ap a linear operator on L^ to L*', Au is defined for u e.
What to read after On the Eigenfunctions of Many Particle Systems in Quantum Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by Tosio Kato to read onlineMoreLess
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