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quant-ph2001★ 5 cited
Testing Hall-Post Inequalities With Exactly Solvable N-Body Problems
Avinash Khare, Jean-Marc Richard
The Hall--Post inequalities provide lower bounds on -body energies in terms of -body energies with . They are rewritten and generalized to be tested with exactly-solva…
quant-ph2001★ 32 cited
Some Exact Results for Mid-Band and Zero Band-Gap States of Associated Lame Potentials
Avinash Khare, Uday Sukhatme
Applying certain known theorems about one-dimensional periodic potentials, we show that the energy spectrum of the associated Lamé potentials $$a(a+1)m~{\rm sn}^2(x,m)+b(b+1)m~{\rm…
quant-ph2001★ 11 cited
A QES Band-Structure Problem in One Dimension
Avinash Khare
I show that the potential $$V(x,m) = \big [\frac{b^2}{4}-m(1-m)a(a+1) \big ]\frac{\sn^2 (x,m)}{\dn^2 (x,m)} -b(a+{1/2}) \frac{\cn (x,m)}{\dn^2 (x,m)}$$ constitutes a QES band-struc…