By Narenda Govil, Ram N. Mohapatra, Zuhair Nashed, A. Sharma, J. Szabados

A suite of over 30 rigorously chosen papers via forty five the world over famous mathematicians, in honor of A. okay. Varma, reflecting his lifelong ardour for investigating polynomials, inequalities in Lp and uniform metrics.

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It is possible to measure ωc of individual particles bound in a Penning trap. The basic conﬁguration of such a trap in shown in Fig. 5. The electrodes and the external magnetic ﬁeld of a Penning trap are such that a charged particle oscillates about the trap center. The eigenfrequencies correspond to oscillations in the z direction, cyclotron-like motion in the plane perpendicular to the z direction, and a slower radial oscillation. It turns out that the cyclotron frequency is sum of the two latter frequencies.

Note that the wavefunction extends far beyond the eﬀective range of the s = 1 nucleon–nucleon potential. −¯ h2 d2 + V (r) u(r) = Eu(r) . 46) √ −2mE . 47) ¯h We set B = 0 to prevent ψ from diverging at the origin and D = 0 to make the wavefunction normalizable. Requiring continuity at r = R of u(r) and u (r) we ﬁnd the condition that determines the allowed values of E u(r > R) ∝ C exp(−κr) + D exp(κr) k(E) cot k(E)R = −κ(E) . 48) We note that for r → 0, the function on the left, k cot kr, is positive and remains so until kr = π/2.

108) 48 1. 4 Quantum theory of conservation laws A quantum system described by a state vector |ψ evolves with time in a way governed by the Schr¨ odinger equation and the system’s Hamiltonian operator H: d|ψ(t) = H |ψ(t) . 109) conspires to conserve a quantity associated with a time-independent operator A. 109) and its Hermitian conjugate. We see that the expectation value is time independent if the operator commutes with H. In nuclear physics, we are generally interested in transitions between states and we would like to see how selection rules that constrain the transitions are generated.