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1. Mathematica Case function in Mathematica

Does anyone familiar with a convenient way in Mathematica to define a case function such as: y(x)=\left\{\begin{array}{c} x \\ -x\end{array}\begin{array}{c} x>0 \\ x<0\end{array} \right. ? Thankes, Omri
2. Scalar field as quantum operator.

Hallo, I was wondering what is the physical significance of scalar field \Phi (x) as an quantum operator. \Phi (x) have canonical commutation relation such as [ \Phi (x) , \pi (x) ] so it must be an opertor, thus what are his eigenstates? Thanks, Omri
3. Editing equations in Mathtype

Hallo everyone, I have a word document full of equations in Mathtype and I added a new equation which I wrote in different size and style. Does anyone know how I can change the old equations (not one by one) so their properties (size, style) would be exactly as those of the new equation...
4. Free electron model

Hallo, i would like to know why do we use the term free electron gas instead of Plasma? aren't both the same? thanks, Omri
5. Soap Bubble and surface tension

I read to today that soap bubbles explodes due to surface tension regardless of other forces experienced on the bubble. how does surface tension does that? does it "drive" the bubble to go larger until it explodes? Thanks, Omri
6. Sphere velocity in liquid-fluid mechanics

Homework Statement a rigid sphere of radius R and density \rho1 mooving (linearly) inside a liquid of densiity \rho0 and viscosity constant \mu the liquid is in hydrostatic equilibrium under gravitational field g. what is the velocity of the sphere after a very long time assuming Raynolds...
7. Why a pair is exciton?

hey, i cant understand what is the motivation of defining pair of hole and electron as a single particle, exciton. thus they seem to have distinct motion and space. so why still we treat them as excitons?
8. Defination of E D and P fields

Hallo everyone, in electrostatic we have a linear realation between E D and P, i do understand that P is related to the polaryzation density but what about E and D? which of those represent the overall field?
9. MATLAB Calling matrices from workspace to For loop in MATLAB

Hallo, I have matrices on my workpace and i need to take the first element from each one and produce new vector. In other words, i have the matrices D1,D2,D3....D36 on my workspace and by using a For loop i want to generate a new vector: d=[D1(1,1) D2(1,1)...D3(1,1)]. does anyone know...
10. C/++/# Random function in c++

Hallo, I'm looking for a Random function in c++. i tried to use in the function rand()% but it does not generate a truly uniformly distributed random number in the span (since my span is large. 100000*100000). in other word it dosent generate a random number in equal probabilty in lage...
11. MATLAB Vectors in matlab

Hallo, I have a 3*3 matrices in matlab: A=[ 1 2 3; 4 5 6; 7 8 9]; and i wont to accept a vector from each colume in an easy way, i.e. a1=1 2 3 , a2=4 5 6 , a3=7 8 9 so i tried to wrote: for i=1:3 a_i=A(:,i); end but i only the last vector, a3=7 8 9... if anyone have...
12. Semiconductors and light effects

A piece of Semiconductor is irradiated by light, will the light effects on resistivity be intensified or reduced if the temprature is increased? why?
13. Y(lm) function

I'm sorry; I have some difficulties with Latex... I have attached Pdf with my question on finding Y(1-1) (l=1,y=-1). Thanks, Omri
14. Continuous partial derivatives

Hallo, What is the condition for partial derivatives to be continuous (if I have function f(x,y))? Thanks, Omri
15. Rolle's Theorem

Hallo. If we consider Rolle's Theorem: "If f is continuous on [a, b], differentiable in (a,b), and f (a) = f (b), then there exists a point c in (a, b) where f'(c) = 0." Why do we need to state continuity of f in interval and differentiability of f in open segment? Why can't we say f...
16. Simple harmonic oscilator

Hallo, Does the velocity i simple harmonic oscillator is zero in equilibrium points? if it's true how does it make sense with the fact that i suppose to get a maximum kinetic Energy in those points (stable ones) i would realy appriciate if someone could clear this issue for me...
17. Uncertainty in simple harmonic oscilator

Hallo, Why can we assume (in the case of simple harmonic occilator) that at the maximum momentum ,pmax, we can evluate pmax=\Deltap? Thanks, Omri
18. W=z^n- transformation in complex space

Hallo, When i regard complex function, Why does the transformation w=zn don't "conserve" angels when z go to infinity? Thanks Omri
19. Interior points

Hallo, My teacher wrote that: "The set has no interior points, and neither does its complement, R\Q" where R refers real numbers and Q is the rationals numbers. why can't i find an iterior point? thanks, Omri
20. Field axioms

hall, i need to prove by using the field axioms that: (-a)(-b)=ab, i think i know how to this but I'm very insecure with using those axioms cause i want to make sure I'm not using my intuition. i tried something like: (-a)(-b)=(-1)(a)(-1)b=(-1)(-1)(a)(b)=ab and i guess it's wrong...
21. First energy level

Hallo. my teacher wrote for the first energy level of a particle in a certain potential \Delta X \Delta P \approx \frac{\hbar}{2} exist. is it a general result for all energy level or there is specific meaning for the first energy level?
22. Infinite potential well

infinite potential well and the uncertainty principle the solution for Schroedinger equation in infinite potential well satisfy the following energy levels: where l is the width of the well. E can't be zero since then \psi=0 so there isn't any particle in the well . i read in...
23. Short circuit

hallo, what is the reason for sparks once i have a high voltage short circuit? Thanks, Omri
24. Electric field of infinite plane

Hallo, Why does the field of a infinite plane does not depend on r? i know it's equal to two \pi\sigma but why does his "infinite" makes it independent on r? thanks Omri
25. Least upper bpunds

Hallo, i read in Spivak that for every upper bounded non empty sets A and B, sup(A+B)=sup(A)+sup(B). but later he wrote other prove which claim that for every function f and g in a close interval exist sup(f+g)<=sup(f)+sup(g) and not necessarily sup(f+g)<=sup(f)+sup(g). how does...
26. Uncertainty principle in classical mechanics boundary

Hallo, Why does dp*dx>>h represents classical mechanics state? Thanks, Omri
27. Magnetic Permeability

What is permeability? I know that it's the ratio between B and H but didn't understand exactly the physical meaning of this concept
28. MATLAB Hysteresis loop on MATLAB

Hallo, If I have an hystersis loop (of ferromagnets) in form of scattered points in matlab what is the function or tool which i can use in order drew a continues hystersis curve(loop)? Thanks, Omri
29. Hysteresis loop

Hallo, Does anyone familiar with an eqution that describs hysteresis loop and First Magnetisation in ferromagnets? Thanks Omri
30. Piston valve Springs in diesel engine.

Hallo, I'm looking for explanation for the fact that in many diesel engines we have two springs supporting the piston valves such that one is exterior and the other interior and they have opposite helical direction. Also if anyone have a link or any information it would be very helpful.