By Pavel Exner, Petr Seba

The shared objective during this number of papers is to use the idea of self-adjoint extensions of symmetry operators in a variety of components of physics. this enables the development of precisely solvable versions in quantum mechanics, quantum box conception, excessive power physics, solid-state physics, microelectronics and different fields. The 20 papers chosen for those complaints provide an summary of this box of analysis unparallelled within the released literature; particularly the perspectives of the prime faculties are sincerely awarded. The booklet can be an enormous resource for researchers and graduate scholars in mathematical physics for a few years to come back. In those complaints, researchers and graduate scholars in mathematical physics will locate how one can build precisely solvable types in quantum mechanics, quantum box idea, excessive strength physics, solid-state physics, microelectronics and different fields.

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Disregard the mass of the string and air resistance. 127. A pendulum consisting of a small heavy bob suspended from a rigid rod oscillates in a vertical plane (Fig. 41). When the bob passes through the position of equilibrium the rod is subjected to a tension equal to twice the weight of the bob. Through what maximum angle on from the vertical will the pendulum be deflected? Disregard the weight of t·he rod and the resistance of the air. 128. A ball of mass m is suspended from a thread of length l.

Both parts of the belt are parallel. —= 15 kW to the pulley. 8. Dynamics of a Point Moving in a Circle Calculating the forces which act on a body moving in a circle is, perhaps, one of the most difficult tasks in physics. The difficulties arise as a rule when the centripetal acceleration in rotational motion and the acceleration in rectilinear motion are regarded as two physical quantities which differ in principle, each obeying its own laws: one can be calculated from the "usual" Newton’s law and the other from the "special" centripetal and centrifugal forces.

When the balls pass through the position of equilibrium the length of the rubber cord becomes equal to that of the thread l (Fig. 47). Which of the balls will have the larger linear velocity when passing through the point of equilibrium? 137. A weightless rod of length l carries first a mass 2m at its end and then two equal masses m, one secured at the 44 PROBLEMS end and the other in the middle of the rod (Fig. 48). The rod can revolve in a vertical plane around the point A-. What horizontal velocity must be imparted to the end of the rod C in the first and second cases to deflect it to the horizontal position?