Recent content by ashok vardhan

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    How Can Plane Wave Solutions Apply in Charged Particle Interactions?

    Hi all, While I am reading interaction of atoms with radiation the following doubt came to me...While solving Maxwell equations in a charge and current free region, we get solutions for Vector potential,Electric field and so on which are plane wave solutions...However, when we study the...
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    Doubt regarding rotations in spinor space

    Dear Sir, I am currently doing an advanced course in Quantum Mechanics. This current doubt of mine, I am unable to clarify it properly. It follows as: Spin 1/2 particles reside in 2dim-Hilbert space( Spinor Space)...However, we talk about rotations of states in this space where the angle...
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    Evaluation of improper integral involving sinx/x

    Sir, Recently when i am evaluating a convolution integral, i came across the integral of |sinx/x| under limits running from 0 to infinity. when i tried to evaluate the integral, i used complex analysis tools like assuming a function e^(iz) / z and deduce the above integral from integral of...
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    Doubt reagarding denseness of a set in (0,1)

    sir, i tried to figure out that 0 is a limit point...but i am stuck with proving the fact that you mentioned i.e for any ε>0,there is ..an element of the sequence such that na<ε..I am able to understand why it should happen..but cannot prove it rigirously..Can u please help me out why such an...
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    Doubt reagarding denseness of a set in (0,1)

    I have been doing a basic math course on Real analysis...I encountered with a problem which follows as" Prove that na(mod1) is dense in (0,1)..where a is an Irrational number , n>=1... I tried to prove it using only basic principles...first of all i proved that above defined sequence is...
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    Is it Possible for a Closed Disk to be Contained in an Open Set?

    Sir , we say that in an open set U for every point (x0,y0) there exists some r>0 such that B((x0,y0),r) lies in U.. where B stands for open disk around (x0,y0) with radiuus r... My doubt is does there exist some "p" such that closed disk around (x0,y0) with radius "p" lies in the open set...
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    Doubt regarding ordered fields

    Sir,i have read in wikipedia that for a relation to be ordered it should be transitive,antisymmetric,total...however we know that Real numbers is an ordered field under relation "<" but antisymmetric property is not valid with "<" relation..how is this justified..rectify me...
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    Doubt in Wheeler's delayed choice experiment

    Sir, I've gone through wheeler's delayed choice experiment recently...i've got few couple of doubts in it..Please clarify them...Actually Wheeler wanted an answer for his questionthat "what happens when a single photon, presumably already determined to get detected as part of a two-slit...
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    Are There Ordered Fields Beyond Real Numbers and Rationals?

    sir , my doubt is that are than any ordered fields other than Real numbers,rational numbers,integers...
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    Doubt about the dimension of a 2nd order homogeneous equation

    sir, i don't know whether i can ask this question in this forum..if not please excuse me..my doubt is i want to learn Complex analysis in details from Basics..which is the best book??
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    Doubt about the dimension of a 2nd order homogeneous equation

    Can anyone help me to clarify my doubt..
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    Doubt about the dimension of a 2nd order homogeneous equation

    My doubt is that is dimension of a 2nd order homogeneous equation of form y''+p(x)y'+q(x)=0 always 2 ? or dimension is 2 only when p(x),q(x) are contionuos on a given interval I..??
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    Prove f(x) Continuous at x=1/2 for x Rational, Irrational

    f(x+y)=f(x)+f(y).f is continuous at x=0.prove that f(kx)=kf(x). i have proved it for k os an integer.for k a rational number i assumed it to be of p/q.and i can't proceed further to prove this. would you like to help in this
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    Find F: R->R satisfying F(x+y)=F(x)+F(y) and F(xy)=F(x)F(y)

    intuitively, the solution is f(kx)=kf(x). i am able to prove it for all integers k.but for a rational number k i am facing problem.so i assumed k to be p/q and later that i can't proced.would you give me a small hint
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    Prove f(x) Continuous at x=1/2 for x Rational, Irrational

    i have already solved the problem in the way you suggested.but i have a problem in solving it using epsilon and those things
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