Unformatted text preview: <  x ] 2 > ψ = R [ x ] 2 [ ψ ( x )] 2 d 3 x , subject to R [ ψ ( x )] 2 d 3 x = 1, and yet allows the energy of a singleelectron atom to be unbounded below. 3. Use the Sobolev inequality T ψ ≥ K s [ Z [ ψ ( x )] 6 d 3 x ] 1 / 3 (2) to ﬁnd a ﬁnite lower bound for the energy of a singleelectron atom. K s is a positive number whose value is not needed. The x ’s are three dimensional vectors. Reference: E.H. Lieb, Rev. Mod. Phys. 48, 553 (1976)....
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This note was uploaded on 12/30/2011 for the course PHYSICS 623 taught by Professor Galitski during the Summer '10 term at Maryland.
 Summer '10
 Galitski
 Physics, mechanics

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