Fundamental Definition and 907 Threads

The initial development of QM inherited the use of complex numbers from Fourier analysis. Had Hartley analysis been invented first, is it possible that QM might have been formulated in terms of real-valued quantities instead, or are complex numbers in some sense natural or necessary when...

I have two full questions on some number theory questions I've been working on, I guess my best bet would be to post them separately. 1) Suppose that n is in N (natural numbers), p1,...,pn are distinct primes, and l1,...ln are nonnegative integers. Let m = p1l1p2l2...pnln. Let d be in N such...

1. Homework Statement Prove that if f(x) is a differentiable real-valued function, and f'(x) is continuous and integrable. Then: \int_a^bf'(x)\,dx = f(b) - f(a) 2. Hint Provided Use the Cauchy Criterion for integrals, the mean value theorem applied to subintervals of a partition, and the...

thanks

Quite a long title :D The fundamental assumption of statistical mechanics states, that all microstates of a system are equally probable. From what I know Liouvilles theorem should support this, but other than that I think it is just a pure assumption. Now I'm not really sure if I find it...

True or false? 1. It is not possible to prove the point of origin of a photon 2. It is not possible to prove the point of origin of a free electron 3. It is not possible to prove that protons or neutrons exist inside a nucleus Can someone please confirm?

Hello; I'm a electrical engineering senior and was wondering if passing the F.E. exam would help in the job market. Since I know it is usually catered toward Mechanical engineering and is requirement for Civil engineers, I'm not sure if it would actually state anything for an emerging...

I teach myself physics. I find it pretty easy but I was getting stuck on this one principle. I was reading about the four fundamental forces of physics. I read that some particles (i.e. Gravitons, gluons, photons, and muons) are force carriers. How would this work? SIDE NOTE I heard that photons...

Homework Statement A 90 cm long steel string with a linear density of 1.1g/m is under 200N tension. It is plucked and vibrates at its fundamental frequency. What is the wavelength of the sound wave that reaches your ear in a 20 degree C room? Homework Equations f = 1/2L * sqrt T/mu v...

Ok so this is kinda wishy washy but I don't know how else to explain this other than I feel like I am missing a critical piece of information as far as fundamental "math" goes. I am highly intelligent and and am a Mechanical Engineering Major who gets all A's, but I feel like I am missing a...

Homework Statement I just learned this idea from my lecture in calculus. I think I understand it at a surface level but don't know much about why it is an astounding discovery as my lecturer suggested. Homework Equations So, it states that let (f) be a continuous on an interval [a,b]. Let...

I was wondering what were the fundamental physical units of measurement, ie those from which all other units can be derived. To my mind, there are only two things which exist in the universe and from which all units of measurement can be derived : space and matter. The reasoning is as follows ...

Can someone explain this please. From what I understand momentum is often the more fundamental as it is spatially invariant, whereas energy is time invariant and as more real world cases fall into the former category momentum is often more fundamental. What is meant by spatial invariance...

Homework Statement I am working on some problems with the fundamental theorem. I need to refresh my memory though, because I have forgotten exactly how to do these problems. I actually am not even sure if I use part 1 or part 2 of the FTC for these problems, so if you could help me in the...

Homework Statement Measurements taken of a square-wave signal using a frequency-selective voltmeter (called a spectrum analyzer) show its spectrum to contain adjacent components (spectral lines) at 98kHz and 126kHz of amplitudes 63mV and 49mV, respectively. For this signal, what would direct...

The world seems to me to be rather arbitrary. I don 't know if people feel the way I do. Scientists apply for government grants to gather data, and conduct experiments. Some scientists look at the data, and write down equations. If those equations are sufficiently fundamental, then some...

Homework Statement problem in attachment Homework Equations The Attempt at a Solution I can get f'(x) as sqrt(1 + (sinx)^2) and derive that to get the second derivative but as far as that I don't really get the concept behind this question will y be another function I have...

Hey Guys, So, I am trying to prove the Fundamental Counting Principle using induction. I have no clue where to start or even how to use induction to prove it. I would appreciate some help. The Question in a mathematical form: Let ^\sharp (A) = m and ^\sharp (B) = n. Proove by induction...

What are the constraints (is this the right word) for introducing new fundamental force? Can our Standard Model accommodate a fifth one? Or would it mess up the math so badly that the present four fundamental forces is the final limit?

A tilted top that would otherwise topple over can somehow not do so if it spins on an axis fast enough, but only if that axis also pivots fast enough circumferentially with respect to a "principal axis". Often conservation of angular momentum is used to predict this. But the rotational pull away...

Homework Statement Let L be a simple compact Lie group, and \Delta_+ is the set of positive roots. I have previously shown that if \alpha\in\Delta_+ and \alpha_i is a simple root, then s_i\alpha\in \Delta_+ where s_i is the Weyl reflection associated with \alpha_i. Now, let \delta =...

Homework Statement The Attempt at a Solution since cos(x^2) is on bottom i flipped it and so it becomes negative. then I got -[(1+cos(x^2))(-sin (x^2))(2x)] substituting with sqrt(pi/2) I keep getting the answer as sqrt(2pi) since the negatives cancel however it says the...

Hi I don't know how to attack the following question, any hints would be appreciated: If G is a simply connected topological group and H is a discrete subgroup, then \pi_1(G/H, 1) \cong H .Thank you James

Homework Statement If I have a solution to a system of first order linear equations: <x,y> = c_1 e^{-3t} <1,-1> + c_2 e^{-t} <1,1> , how do I find the fundamental matrix psi(t) so that psi(0) = I ? Homework Equations The Attempt at a Solution psi(t) = <<e^{3t}, e^{-t}>...

If f is continuous on [a,b] then the function g defined by g(x) = ∫f(t)dt a <= x <= b is continuous on [a,b] and differentiable on (a,b) and g' = f Question... If f is continuous on [a,b], then why is g only differentiable on (a,b)? This does not make sence... if g' = f g should be...

It is proved in this topic (last answer): https://www.physicsforums.com/showthread.php?t=536987

Homework Statement The fundamental frequency of a stretched string is 200Hz. when the length of the string is doubled and Tension of the string made 100times the initial Tension, what is the new fundamental frequency of the string. (1) 50 Hz (2) 100 Hz (3) 200Hz (4) 400 Hz (5) 800 Hz...

what is the most important fundamental quantity

I think a best informal way to state the theorem is Hardy's: every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of one or more primes But clearly, this statement does not reveal the structure of the statement in the formal...

No idea what to do here, really tough question, can i get some assistance please? Homework Statement The equation of a traveling transverse wave is y=2.0sin 2π(x/30 - t/0.01) where x and y are in centimetres and t is in seconds. When attached at both ends, a string under a tension...

what i'd like to know is simply put this way: is energy fundamental or emergent? but more importantly, this is a fact or fiction question seeing as they (fundamental and emergent) are oposites, so can we all agree on one answer? what i mean is whatever your "opinion" at the end of the day...

What would be the most fundamental equations in physics? For example, I know that all of electrodynamics can be obtained from Maxwell's Equations; therefore, Maxwell's Equations would be a complete set of the most fundamental equations of EM. However, something like PV=nRT can be derived from...

This is not a question I need to work out but I'm trying to understand this theorem. My lecture notes state: 'This theorem states the existence of solutions to the Frenet - Serret Equations that, apart from the possibility of a rigid motion, are uniquely determined by any choice of smooth...

I was asked this question by someone else and wondered if I could get better answers here: Is it fair to say that the standard model for matter is basically descriptive, without any underlying understanding of what causes its structure? Can it be compared it to the periodic table of...

My Fundamental Math Failing This should illicit a chuckle or perhaps despair in humanity. The statement "One silver piece is equivalent to two copper pieces" is not equivalent to the equation "S = 2C" (Where S = silver and C = copper). I cannot for the life of me figure out why. I can work...

*using complex analysis. (sorry couldn't post the entire thing in the thread title). It seems there is a common proof of the fundamental theorem of algebra using tools from complex analysis, namely Louisville's theorem and the max. modulus theorem. Here is an example proof from proof wiki...

Homework Statement Two open tubes both have actual length 1m but their diameters are D=1 cm and D=10 cm. Alowing fro end corrections, what are their fundamental frequencies? Homework Equations the only equation in my book that deals with Diamter is N(Critical...

Homework Statement How many natural numbers are there with the property that they can be expressed as the sum of the cubes of two natural numbers in two different ways. Homework Equations N/A The Attempt at a Solution I don't understand how should i start. :( Can somebody give...

So I want to get all the Equations that describe classical Physics together because I think it would make a kick *** poster. Tell me if I am missing anything or if you don't think one should be on here. [PLAIN]http://img694.imageshack.us/img694/9646/classicalequations.gif

I read the following in Fowles & Cassiday's Mechanics: "The correct motion that a body takes through space is that which minimizes the time integral of the difference between the kinetic and potential energies" or \deltaJ = ∫ L dt = 0...

If one were to subtract the kinetic energies of all fundamental particles within hydrogen, as well as all of the potential energy of all bound states between these particles, how much mass (as a percentage of the total) would remain? Ignore the kinetic energy due to the hydrogen's speed.And...

Show that there are two abelian groups of order 108 that have exactly one subgroup of order 3. 108 = 2^ 2 X 3 ^ 3 Using the fundamental theorem of finite abelian groups, we have Possible abelian groups of order 108 can be : Z108, Z4 + Z27, Z2+Z2+Z27, Z4+Z9+Z3, Z2+Z2+Z9+Z3, Z4+Z3+Z3+Z3...

Hello, trying to figure out exactly what is going on in this question. Homework Statement (a) If P(z) is a nonconstant polynomial, show that |P(z)| > |P(0)| holds outside some disk R |z| ≤ R for some R > 0. Conclude that if the minimum value of |P(z)| for R z ≤ |R| occurs at z_o...

Hello, I just need help deriving the fundamental equation from Equation of state for wan der waals fluids. P=\frac{RT}{v-b}-\frac{a}{v^2} and u=cRT-\frac{a}{v} where a,b, and c are constants. I know the fundamental equation is dS=\frac{1}{T}dU+\frac{P}{T}dvI solved the u equation so it's...

Hello, if I have a fundamental solution, ,f, to a partial differential equation L(f)=0, where L is the differential operator, is that true that the derivatives of the fundamental solution, like D(f), will also be solution to the partial differential equation? Intuitively, is it because things...

Homework Statement Shown in Picture attachment Question number 6 Homework Equations Not sure..I'm fresh on physics at the moment.. :( The Attempt at a Solution Givens T1 = 250N T2 = 160N L1 = 45cm L2 = 56cm f1 = 450Hz f2 = ? I'm pretty clueless at the moment.. :(

I read in this weeks Time (or maybe it was Newsweek) a statement that I have heard numerous times over the years and dismissed as nonsense but it occurred to me now that it has been 45 years since I took college physics and maybe I'm remembering something incorrectly, although I don't think so...

Take 4 pennies and 2 dimes. Now assume that you have no way to distinguish the pennies from each other and no way to distinguish the dimes from each other, but you can tell the difference between a dime and a penny. For each of the following situations, how many different ways can you pull...

A block is resting on a frictionless surface as shown in the figure attached with this post. Calculate the minimum force F required so that the block will topple? The dimensions of the block, free body diagram and other details are there in the picture attached. Now, since the surface is...

If somthing falls 10 meters (at 10m/s), ignoring air resistance, why does it take 1.4s to land instead of just one? I suppose i am simply having a brain fart but this is bothering me...