physics-subatomic-particles

after this experiment, W .Zinn showed that neutrons were also subject to de Broglie' sequation . Neutrons from a chain-reacting pile were slowed down by graphite blocks ,and were then collimated by a series of cadmium slits . They were then reflected fro mthe face of a calcite crystal, and detected by means of a boron trifluoride counter .In 1926, two comparatively contemporary theories of particles as waves grew up .The first was the matrix mechanics of ;.Heisenberg, and the second the wave equation o f: .Schrtldinger . Although very different in their approach, Schrddinger, as we shal ldiscuss later, finally showed that the two theories were equivalent . We shall firs tdiscuss the SchrBdinger equation, because it is the simpler of the two methods . As i twas first formulated, the Schrtldinger equation made two assumptions about the particl esystem which it attempted to describe . First, it assumed that no particles were eithe rcreated or destroyed, and that therefore the number of particles of a given type i nour system always remained constant, and second, that the velocities of all th eparticles concerned were small enough for non-relativistic approximations to be valid .We represent our wave function by 14r(x, t) . Born's interpretation of this wave functio nstates that the probability that we find our particle in a small region of space ,volume d3 (x) is proportional toh4r(x,t) l l d; (x) . Thus the probability density i sproportional to the absolute square of the wave function . Similarly the intensity ofa classical light wave is said to be proportional to the square of its amplitude .There was at first considerable discussion concerning the reality of mechanical waves ,but Born's idea puts this aside . It implies that the wave-like character of particle sis essentially to do with the fact that the probability function If satisfies a wav eequation . Thus, if we have, for example, a shower of scattered electrons, we may sa ythat if there are a large number of particles, we are most likely to find particles i nthe regions where the absolute squares of their wave functions are large . The probab -ility of finding a particle in a space, volume dxdydz units, is defined as dxdydz .As the particle must exist somewhere in space, and as most probabilities are measure das a fraction of unity, it is natural that we should apply what is known as anormalisation factor in order to make S~1fr dxdydz equal to one . In fact, Schrddinger' swave equation was defined such that :iM 1-(x t) = - LV''y1(x,t)2sl,where i is the square root of minus one, h is Planck's constant, and 'eis the Laplacianoperator, which is defined by :®1— a1+ V.4 VLax,Sxi bx iLet us now discuss an important principle in wave mechanics known as the super -position of waves . A light beam is very rarely truly monochromatic . Thus, its classicalwave is not pure, but consists of a number of partial waves, each of a differen tfrequency, superposed on each other . A pure wave has a well-defined energy given b ythe Planck- ;instein formula, and thus, in a superposed wave, the intensity of each o fits partial waves is a measure of the probability that the complete wave has the sam efrequency as that wave at the moment when it is measured . Using a superpositionmethod, Schrtldinger showed that Bohr's model of the atom could be derived using wav emechanics, because all the waves of the electrons must be stationary or standing waves .A standing wave is one in which there are a number of fixed nodes, between whic hoscillations take place .,fie must now consider the more important consequences of W .IIeisenberg's matri xmechanics, which he developed in 1923, while studying under M .Born at GBttingen .Heisenberg realised that very little was known about atoms, except for the nature of