QuantumPhysics.dvi

the spectrum. We do not assume, however, thatE^0 n′=En^0 , so that we can applynon-degenerate perturbation theory. First order p ...

11 External Magnetic Field Problems In the chapter on perturbation theory, we have studied the effect of small magnetic fields o ...

and the partition function will diverge in this limit. Below, we investigate in the operator language, the phenomenon that drive ...

11.2 Complex variables Thex,yparts of the combinationsaandbcorrespond to forming the complex variables z= 1 √ 2 (x+iy) pz= 1 √ 2 ...

11.3 Calculation of the density of states in each Landau level An important characterization of the Landau levels is the number ...

Here,meis the electron mass andvits velocity. The last term account for the dissipative processes which lead to Ohm’s law, and w ...

Figure 11: Schematic representation of the Hall and regular conductivity in the integer quantum Hall effect. (from R.E. Prange i ...

The fundamental unit of 2-dimensional resistivity may be readily evaluated, using ̄h= 1. 05457 × 10 −^34 Jsande= 1. 60218 × 10 − ...

Figure 12: Actual experimental results exhibiting integer and fractional quantum Hall effects. (from A.M. Chang inThe quantum Ha ...

wave function of theNelectrons be anti-symmetric under the interchange of any two coordinates ziandzjforj 6 =i. The following wa ...

12 Scattering Theory Bound state perturbation theory, discussed in the preceding chapter, has allowed us to understand the energ ...

orEcm ∼ √ 2 EMc^2 for high energy. The linear energy dependence for a colliderwins over the square root dependence of the fixed ...

To solve (12.3) perturbatively, we move the perturbative correction piece to the right hand side of the equation, (H 0 −E)|ψk〉=− ...

12.3 The free particle propagator In almost all cases,^11 H 0 will be the Hamiltonian for a free probe of massm, H 0 = P^2 2 m ( ...

The factor of 4πgives the correct normalization for theδ-function. Fork^26 = 0, rotation invariance of the Fourier integral show ...

and the solution to all orders is ψ = φ+GUφ+GUGUφ+··· = φ+ ∑∞ n=1 (GU)nφ (12.27) The interpretation of the first term is free pr ...

Electro-magnetic: long-ranged; the mediator is the massless photon. Weak interactions: short-ranged; the mediator are the massi ...

Using the time-dependent Schr ̈odinger equation, i ̄h ∂ψ ∂t =− ̄h^2 2 m ∆ψ+V ψ (12.34) one shows conservation of this current, ∂ ...

wherec.c.stands for the complex conjugate of the preceding term. In carrying out the∇derivative with respect to the variablex, s ...

Its form is very simple, sincef(1)(k′,k) is proportional to the Fourier transform of the potential evaluated onk′−bkwhich is pro ...