TAILIEUCHUNG - The Quantum Mechanics Solver 10

The Quantum Mechanics Solver 10 uniquely illustrates the application of quantum mechanical concepts to various fields of modern physics. It aims at encouraging the reader to apply quantum mechanics to research problems in fields such as molecular physics, condensed matter physics or laser physics. Advanced undergraduates and graduate students will find a rich and challenging source of material for further exploration. This book consists of a series of problems concerning present-day experimental or theoretical questions on quantum mechanics | Solutions 85 . Given the definitions of wq and iL one has 2 2 WQ 2 . 9 Iv q7 2 4 V Mqe ac 2 Bq2 f 2 n EQ where a is the fine structure constant and c the velocity of light. The experimental line ac 3 2BQ2 f 2 34 Eq2 goes through the points E2 0 B2 87 x 10 -4 T2 and B2 0 E2 4 x 106 V2m 2. This gives f 34 34. . Indeed the very simple result found by Pauli was f n n. 10 Energy Loss of Ions in Matter When a charged particle travels through condensed matter it loses its kinetic energy gradually by transferring it to the electrons of the medium. In this chapter we evaluate the energy loss of the particle as a function of its mass and its charge by studying the modifications that the state of an atom undergoes when a charged particle passes in its vicinity. We show how this process can be used to identify the products of a nuclear reaction. The electric potential created by the moving particle appears as a timedependent perturbation in the atom s Hamiltonian. In order to simplify the problem we shall consider the case of an atom with a single external electron. The nucleus and the internal electrons will be treated globally as a core of charge q infinitely massive and therefore fixed in space. We also assume that the incident particle of charge Z1q is heavy and non-relativistic and that its kinetic energy is large enough so that in good approximation its motion can be considered linear and uniform of constant velocity v when it interacts with an atom. Here q denotes the unit charge and we set e2 q2 4ne0 . We consider the x y plane defined by the trajectory of the particle and the center of gravity of the atom which is chosen to be the origin as shown on Fig. . Let R t be the position of the particle at time t and r x y z the coordinates of the electron of the atom. The impact parameter is b and the notation is specified in Fig. . The time at which the particle passes nearest to the atom . x b y 0 is denoted t 0. We write En and n for the energy .

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