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[4] Y.S. Jain: “Untouched aspects of the wave mechanics of two particles in a many body quantum system”, J. Sc. Explor., Vol. 16, (2002), pp. 67–75.
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[5] Y.S. Jain: “Basic problems of microscopic theories of many body quantum system”, cond-mat/0208445 (www.arXiv.org), pp. 1–9.
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[6] Y.S. Jain: “Microscopic theory of a system of interacting bosons: a unified approach”, J. Sc. Explor., Vol. 16, (2002),pp. 77–115.
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[7] Y.S. Jain: “Unification of the physics of interacting bosons and fermions through (q,-q) pair correlation”, J. Sc. Explor., Vol. 16, (2002),pp. 117–124.
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[8] Motions of P1 and P2 (HC size, σ) relativer to their CM can be represented by a superposition of a plane wave of momentumq with one of momentum −q (a reflected wave fromV HC (x)). Correcting such a waveform,v k (x)=sin (qx)=sin (kx/2), for σ size, we getw′ k (xCM (1)≥σ/2)=sin [k(xCM (1)−σ/2)] (withw′ k (xCM (1)<σ/2)=0) for P1 andw″ k (xCM (2)≤−σ/2)=sin [k(|xCM (2)|−σ/2)]) (withw″ k (xCM (2)>−σ/2)=0) for P2. One can express bothw′ andw″ by a single waveformw k (|x|≥σ)=sin[k(|x|−σ)/2] withw k (|x|<σ)=0 whith in the limit σ→0 becomesw k (x) = sin (k|x|/2) = |sin(kx/2)| =φ k (x)+; here we use Eqn. 8 withx=xCM (1)−xCM (2). Note thatw k (|x|<σ)=0 holds good if the occupancy of space by P1 and P2 is identified with the points occupied by the centres of their HC spheres, but the fact remains that all points (excludingx=0) covered by |x|<σ remain occupied by P1 and P2 when these centres are at |x|=σ.
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[9] P. Kleban: “Excluded volume conditions in quasi-particle theories of superfluidity”, Phys. lett., Vol. 49A, (1974), pp. 19–20.
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[10] L.I. Schiff: Quantum Mechanics, 3rd ed. McGraw Hill, New York, 1968.