1000 Solved Problems in Modern Physics by Ahmad A. Kamal

By Ahmad A. Kamal

This ebook primarily caters to the desires of undergraduates and graduates physics scholars within the zone of contemporary physics, specifically particle and nuclear physics. Lecturers/tutors may possibly use it as a source publication. The contents of the ebook are in keeping with the syllabi at present utilized in the undergraduate classes in united states, U.K., and different nations. The publication is split into 10 chapters, every one bankruptcy starting with a quick yet sufficient precis and useful formulation, tables and line diagrams via quite a few common difficulties precious for assignments and checks. designated suggestions are supplied on the finish of every chapter.

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The linear differential equation of the first order is of the form dy + Py = Q dx where P, Q are functions of x alone, or constants, the solution is given by ye Pdx = Qe Pdx dx + C 18 1 Mathematical Physics Type IV equations reducible to linear form Some equations that are not linear can be reduced to the linear form by a suitable substitution, for example ( A) dy + P y = Qy n dx where P, Q are functions of x alone, or constants. Equation ( A) may be reduced to the linear form (A), Type III by means of the substitution x = y −n+1 .

Complex variables Complex number z = r (cos θ + i sin θ), where i = z n = cos nθ + i sin nθ √ −1 Analytic functions A function f of the complex variable z is analytic at a point z o if its derivative f (z) exists not only at z o but at every point z in some neighborhood of z o . As an example if f (z) = 1z then f (z) = − z12 (z = 0). Thus f is analytic at every point except the point z = 0, where it is not continuous, so that f (0) cannot exist. The point z = 0 is called a singular point. Contour A contour is a continuous chain of finite number of smooth arcs.

B) where C is an arbitrary constant. 1 Basic Concepts and Formulae 17 Equations which are not in the simple form ( A) can be brought into that form by the following rule for separating the variables. First step: Clear off fractions, and if the equation involves derivatives, multiply through by the differential of the independent variable. Second step: Collect all the terms containing the same differential into a single term. If then the equation takes on the form X Y dx + X Y dy = 0 where X, X are functions of x alone, and Y, Y are functions of y alone, it may be brought to the form ( A) by dividing through by X Y .

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