By Hiroomi Umezawa

This paintings starts off by means of distinguishing the adaptation among quantum mechanics and quantum box concept. It then makes an attempt to increase box concept through including a thermal measure of freedom to phenomena happening inside a vacuum. The ensuing quantum box conception is termed Thermo box Dynamics (TFD).

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**Sample text**

1 Deﬁne the characteristic of the elementary inelastic process for the transition of a particle A between the states i and f as a result of collision with a particle B. Let us consider a motionless particle A located in a gas of particles B, and interaction with these particles cause the transition between the indicated states. 1) where νif is the rate (the probability per unit time) of a transition. The rate νif of transition is proportional to the ﬂux j of particles B, which collide with a test particle A.

As a matter of fact, it is an integral form of the Schrödinger equation. But this representation of the wave function is convenient, because it allows us to transfer to the limit of large R. In the limit R → ∞ we have R − R = R − R n, where n is the unit vector directed along R. 10) and this is a general expression for the wave function far from the scattered center. Here the ﬁrst term is an incident wave, the second term is a scattered wave, the value f (ϑ) is the scattering amplitude, which is responsible for particle scattering, and ϑ is the scattering angle between the vectors R and q.

12) Thus, the diﬀerential cross section of elastic scattering is connected with the scattering amplitude in a simple way. 10 Find the amplitude of elastic scattering of particles within the framework of the perturbation theory. 11) the wave function of particles in the absence of interaction, when the wave function has the form of a plane wave ψ(R) = eiqR . This gives for the scattering amplitude f (ϑ) = − µ 2π¯h2 e−iK R U(R )dR . 13) is named the Born approximation. The relation between the wave vector variation K and the scattering angle ϑ is K = 2q sin(ϑ/2).