Đây là bộ sách tiếng anh về chuyên ngành vật lý gồm các lý thuyết căn bản và lý liên quan đến công nghệ nano ,công nghệ vật liệu ,công nghệ vi điện tử,vật lý bán dẫn. Bộ sách này thích hợp cho những ai đam mê theo đuổi ngành vật lý và muốn tìm hiểu thế giới vũ trụ và hoạt độn ra sao.
[...]... coordinate and linear momentum in < /b> one dimension Evaluate the classical Poisson bracket x F (px)]classical : (b) Let x and px be the corresponding quantum-< /b> mechanical operators this time Evaluate the commutator x x exp iph a : (c) Using the result obtained in < /b> (b) , prove that x exp iph a jx0i (xjx0i = x0jx0i) 1 FUNDAMENTAL CONCEPTS 33 is an eigenstate of the coordinate operator x What is the corresponding eigenvalue?... Suppose the system is in < /b> j + ;i for t 0 Find, as a function of time, the probability for being found in < /b> each of the following states j + +i, j + ;i, j ; +i, j ; ;i: (a) By solving the problem exactly 5 APPROXIMATION METHODS 21 (b) By solving the problem assuming the validity of rst-order time-dependent perturbation theory with H as a perturbation switched on at t = 0 Under what condition does (b) ... corresponding energy to < /b> rst order that is the unperturbed energy obtained in < /b> (a) plus the rst-order energy shift] for each of the three lowest-lying states (c) Solve the H0 + V problem exactly Compare with the perturbation results obtained in < /b> q (b) p < /b> 0 jxjni = h=2m! (pn + 1 0 + n 0 ):] You may use hn n n+1 n n;1 5.2 A system that has three unperturbed states can be represented by the perturbed Hamiltonian matrix... of your expression is independent of time Is this reasonable or surprising? (b) Can we nd higher excited states? q You may use hn0jxjni = h=2m! (pn + 1 n0 n+1 + pn n0 n;1 ):] 1 5.4 Consider a composite system made up of two spin 2 objects for t < 0, the Hamiltonian does not depend on spin and can be taken to < /b> be zero by suitably adjusting the energy scale For t > 0, the Hamiltonian is given by ~ ~ H... 1)! ia px = ;a exp iph a : (1.42) h n=1 (c) We have now b x x x x exp iph a jx0i (=) exp iph a xjx0i ; a exp iph a jx0i x x = x0 exp iph a jx0i ; a exp iph a jx0i x = (x0 ; a) exp iph a jx0i: (1.43) x So exp iph a jx0i is an eigenstate of the operator x with eigenvalue x0 ; a So we can write x (1.44) jx0 ; ai = C exp iph a jx0i where C is a constant which due to < /b> normalization can be taken to < /b> be 1 34... Prove the minimum uncertainty relation for such a state (c) Write j i as 1 X j i = f (n)jni: 2 n=0 Show that the distribution of jf (n)j2 with respect to < /b> n is of the Poisson form Find the most probable value of n, hence of E (d) Show that a coherent state can also be obtained by applying the translation ( nite-displacement) operator e;ipl=h (where p < /b> is the momentum operator, and l is the displacement... degenerate perturbation theory Compare the three results obtained 5.3 A one-dimensional harmonic oscillator is in < /b> its ground state for t < 0 For t 0 it is subjected to < /b> a time-dependent but spatially uniform force (not potential!) in < /b> the x-direction, F (t) = F0e;t= (a) Using time-dependent perturbation theory to < /b> rst order, obtain the probability of nding the oscillator in < /b> its rst excited state for t >... restrictions do we obtain on Flm(r)? 4.5 The Hamiltonian for a spin 1 system is given by 2 H = ASz2 + B (Sx ; Sy2): 5 APPROXIMATION METHODS 19 Solve this problem exactly to < /b> nd the normalized energy eigenstates and eigenvalues (A spin-dependent Hamiltonian of this kind actually appears in < /b> crystal physics.) Is this Hamiltonian invariant under time reversal? How do the normalized eigenstates you obtained transform... (b) By comparing the Hamiltonian and the commutation relation obtained in < /b> (a) with those of the one-dimensional oscillator problem show how we can immediately write the energy eigenvalues as ! h2k2 + jeB jh n + 1 E = kn 2m mc 2 where hk is the continuous eigenvalue of the pz operator and n is a nonnegative integer including zero 2.15 Consider a particle of mass m and charge q in < /b> an impenetrable cylinder... erences between this problem and the (more realistic) photoelectric e ect (note: For the initial wave function use 1 Z 2e;Zr=a0 : x n=1 l=0 (~ ) = p < /b> a0 3 If you have a normalization problem, the nal wave function may be taken to < /b> be 1 x f (~ ) = L 3 2 px ei~ ~=h with L very large, but you should be able to < /b> show that the observable e ects are independent of L.) 22 Part II Solutions < /b> 23 1 FUNDAMENTAL CONCEPTS . class="bi x0 y0 w1 h1" alt=""