equation Definition and 125 Threads

I have been fascinated with the Schrodinger equation for years - in self-study mode. Lots of notes, a couple of papers which never appeared in print. That interest continues. In spite of Stack Exchange's response, I constinue to continue to work on the problem, and we'll see where that goes.

In telecommunication system there's a fresnel zone, it's an area between transmitter and receiver (i'm sure all the experts in this forum already knew about that). So, in this website (Fresnel Zone Calculator - everything RF) provide a Fresnel Zone Calculator, it also tells the equation, which...

My solution: Let ##f(x+y)=f(x)f(y)-[f(x)+f(y)]-1/2## İf ##y=x## we find functional equation that given us. So for ##x=y=1## then ##f(2)=-1/2## İf we evaluate ##x=1, y=2## at above equation ##f(3)=-3## My question is: What is the solution of that functional equation; I mean are there other...

I rearranged the equation and got $$12x+12y=xy$$ Differentiating this I get $$12\frac{dx}{dt} + 12\frac{dy}{dt} = x\frac{dy}{dt} + y\frac{dx}{dt}$$ Substituting the values I get $$12\frac{dx}{dt} -12= -5+\frac{dx}{dt}$$ SO $$\frac{dx}{dt}=\frac{7}{11}$$ But if I directly differentiate the...

Hi, I am doing a sine quation which has multiple numbers along the line.I was wondering when multiplying the equation out do I multiply all the numbers then sin function that number or do I sin the number beside the sine function and then multiply it out? The equation is: sin h bt/ bt. I also...

I tried to use Taylor expansion to see what would happen to the equation, but I kept having problems with the term (hν/kT)² Have a nice day, everyone!

Dear all, I have a rather basic question about an equation in David Tong's lecture notes on cosmology; see http://www.damtp.cam.ac.uk/user/tong/cosmo.html My question is about eqn. 1.19 (page 14), in which the cosmological redshift is derived. It's not about the physics, but about some basic...

and its proposed solution: Now the first equation seems to be ##\dot{\lambda}=-H_{x}##, but they seem to forget to divide by two ##(3x^2+u^2)##, and the second equation, I am not sure how did they derive the second equation of ##u=-\lambda##? anyone here knows how? thanks!

What do you interpret from this equation. G μν(g αβ)+Λg μν= 8πG/C^4 T μν({φ i,θ i}) Spacetime geometry = Interference-driven stress-energy>> I'm not looking for conformation. Just a little help n interpretation. Plz

It looks like a mistake, the book writes the following: I believe (2.4) should be: ##F(\omega)=\gamma Q(\omega)+(1-\gamma)F(\omega)Q(\omega)##. I don't understand these pitfalls in books, they don't make someone to proof-read the text?! I mean besides me the reader... of course. :-D

Tt's easy to see permutations of ##(1,0,0)## are trivial solutions. I can use ##a^3+b^3+c^3=3abc+(a+b+c)(a^2+b^2+c^2-ab-ac-bc)## and I can find ##ab+ac+bc## in terms of ##a+b+c## but how can I achive the same thing for ##abc##?

Griffiths Pg 133 4th Edition Why can't n be negative? Is there a reason for this? My thought is that if n is negative, as sine is odd, the negative gets absorbed into C, a constant. Is this correct? Would it be equally correct to let n be a negative integer? Thank you

I have a question about the neutron transport equation, my question is more about mathematics, from the book Duderstadt Hamilton I tried to make the calculations, it should be quite simple but still I don't understand where the 2\pi terms went... the integral over Omega in spherical...

I have no idea for this question. Can you give me some clue, please?

I can find f(0)=1 and f(1)=2 and f(7)=128. I Wonder how can I find f function?

I came across an equation in a disconnected piece of my notes, and I remember that it was an instance of something, but I can't remember what. (I see how to do the integration, that is not what I am worried about.) Does anyone recognize either the function or the integration as an example of...

Hi everyone, I am going through the book called "Numerical Methods for Engineers" and I am trying to solve for the angle of displacement of a pendulum. I am using MATLAB to do this. However, I am getting some strange results. In the book the differential equation is: Because this is a...

This is a simple question, but after 30 minutes on Google, no sensible results. I want to solve this equation: 1/(2.04Sin(29.36 + 0)) on a regular basis. My idea was to have that term as a Google search, saved as a bookmark. The idea has worked well for years for another formula, but without...

I am trying to follow through a derivation of the solution to the wave equation governing a string with fixed ends via separation of variables but I am stuck at the step which concludes ‘m’ must be a natural number 1,2,3,… etc. as opposed to an integer. After analysing each case: m > 0, m = 0...

Hello. General form of the equaion is ## i \hbar \dfrac {\partial}{\partial t} | \psi (t) \rangle = \hat H | \psi (t) \rangle ## According to my book ## \hat H ## in position space is ## - \dfrac {\hbar ^2}{2m} \nabla^2 + V( \hat {\vec R} , t)## so potensial V is a function of operator...

After collision energy is mgh/2. I am having trouble in writing the energy equation after this.

Let's denote ##\sqrt[3] r =t##. The three expressions above can be written as $$x_1=2t \cos \frac {\phi} 3, x_2=t (-\cos \frac {\phi} 3 -\sin \frac {\phi} 3), x_3=t (-\cos \frac {\phi} 3 +\sin \frac {\phi} 3)$$ The Vieta's formulae for the given equation are $$x_1+x_2+x_3=0$$ $$x_1 x_2+ x_2 x_3...

If the laws of physics say that nothing can move faster than the speed of light, how can we square it in Einsteins equation? It dosent make synce to me. How does Einsteins equation work can someone break it down for me and explain it in layman’s terms please. How can we warp spacetime just by...

TL;DR Summary: Exponential VS Logarithmic Regression (using the TI-84 Plus graphing calculator) Here is the question: A scientist examines the growth of bean plants under different growing conditions. The results of one trial are as follows: Day...

Proof: Consider the equation of ## a^2-x^2=\epsilon\sinh x ## for ## 0<\epsilon<<1 ##. Let ## \epsilon=0 ##. Then the unperturbed equation is ## a^2-x^2=0 ##. This gives ## a^2-x^2=0\implies (a+x)(a-x)=0\implies x=\pm a ## with the root ## x=x_{0} ## such that ## x_{0}(a)=a ## because ## x\geq...

a) Proof: By definition, the potential energy ## V(x) ## is given by ## F(x)=-\frac{dV}{dx} ##. Note that ## \ddot{x}=-\frac{dV}{dx} ## where ## \ddot{x}=-x-\epsilon(\alpha x^2\operatorname{sgn}(x)+\beta x^{3}) ##. This gives ## \frac{dV}{dx}=x+\epsilon(\alpha x^2\operatorname{sgn}(x)+\beta...

I've tried a few things. I did one method to try to accomplish the removal of the -70 in the derivative boundary condition. It came out as below. When plotting it however it gave a solution that didn't make sense.

(Yes, I'm guilty of passing along something incomplete and of utterly unknown provenance that someone saw somewhere and didn't understand. I feel dirty.) ∀t(T(x,t)⟹(¬H(x,t)∨H(x,t+Δt))) Certainly, without specifying any of the variables, it's got to be useless. At least we can assume t and Δt...

Was the approach used by the referenced tutor correct? In my understanding, the set up equation ought to be, ##s=-h, u=16## as the stone is being thrown upwards and ##g=-9.8## giving me, ##-h = 64 - \dfrac{1}{2}×9.8 ×16## ##-h=-14.4##m ##h=14.4##m , or it does not really matter.

I need an idea. Thank you.

The paper follows (free): https://arxiv.org/abs/2111.03203v2 I was trying to read it, but couldn't understand where equation 2 comes from (page 3). Is this just a standard diffraction or interference equation? Could anyone provide a reference that explains that equation?

My attempt and solution : $$2^x=3^y+509\Longrightarrow 2^x-512=3^y+509-512\Longrightarrow 2^x-2^9=3^y-3$$ $$\Longrightarrow 2^9(2^{x-9}-1)=3(3^{y-1}-1)$$ $$\Longrightarrow (x,~y)=\boxed{(9,~1)}$$ İs there any solution?

Would we also use Newton's method, or are there more powerful methods? Are there general methods for solving equations with fractional exponents? The solution to this problem is; https://www.wolframalpha.com/input?i=solve+x%5E%2817%2F6%29+%2B+x%5E%2821%2F25%29+%3D+15

Is there a better way of solving this, My steps, ##5(x+1)^{1.5}-4x-28=0## ##(x+1)^{1.5}=\dfrac{4x+28}{5}## ##(x+1)^3=(\dfrac{4x+28}{5})^2## ##x^3+3x^2+3x+1=\dfrac{16(x+7)^2}{25}## ##25x^3+75x^2+75x+25=16(x^2+14x+49)## ##25x^3+59x^2-149x-759=0## Letting ##f(x)=25x^3+59x^2-149x-759=0## and using...

I’ve found that when I use g(x)= (x+3)(x-1)2 You get everything except the maximum x=-1 I just cannot get that last one

I figured since ## dr/dt ## is simply the velocity of the target mass, the velocity ##u_x## would simply have to be changed by the Lorentz transformation. Since the rest mass doesn't change, I think this should be as simple as taking the Lorentz transformation for velocity, and substituting the...

Proof of kinetic energy work done equals a change in kinetic energy in a mechanical system. δW = F.ds W = ∫F.ds W = m∫a.ds W = m∫(dv/dt).ds W = m∫v.dv here if v and dv are in the same direction the change in kinetic energy will be the usual equation. what happens if both are in different...

I'm currently taking Math Methods in Physics, and we're working on infinite series right now. In one of the examples, in order to find the limit, they do what you can see below in "Example 3" As you can see, they turn the original equation into a ln equation, so that they can bring the...

I have this expression, $$T=2 P r-\frac{q^2}{4 \pi r^3}+\frac{1}{4 \pi r}$$. Now I want to solve this equation for ##r## perturbatively. This will give the expression $$r=\frac{T}{2 P}-\frac{1}{4 \pi T}+\frac{P \left(8 \pi P q^2-1\right)}{8 \left(\pi ^2 T^3\right)}+.......$$. I was reading...

I initially thought about the different forms of energy present at each of the points: Total energy at starting point: PEA+ KEA= mgH at point D: KE_D = 1/2mv2f PED= mgD Energy at point D: PED+ KED D = mgD + 1/2 mv2f because EA= ED mgH = mgD = 1/2 mv2f mg(H-D) = 1/2 mv2f g(H-D) = 1/2...

Proof: Let ## x=\sqrt[3]{18+\sqrt{325}}+\sqrt[3]{18-\sqrt{325}} ##. Then ## x^3=(\sqrt[3]{18+\sqrt{325}}+\sqrt[3]{18-\sqrt{325}})^3 ##. Note that ## (a+b)^3=a^3+3ab(a+b)+b^3 ## where ## a=\sqrt[3]{18+\sqrt{325}} ## and ## b=\sqrt[3]{18-\sqrt{325}} ##. This gives ##...

I can imagine x + y = 1 to be line in xy - plane but how can x + 2y + z = 3 be a line, not a plane? Thanks

Where can I find detailed derivation of Field Equation of Teleparallel Gravity from variation of Action ?

I've seen a lot of people use implication and equivalence logic incorrectly. For example, when solving equations (i.e. ##x - 2 = 3 \implies x = 5##). Implication is not reversible, thus it only works in one way. By saying, ##x - 2 = 3 \implies x = 5##, you are essentially saying that it is...

Balancing the complete combustion of acetic acid equation to carbon dioxide and water is straightforward if you remember hydrogen is always +1, elemental oxygen is zero and combined oxygen is always -2. just balance the exchange of electrons between oxygen and carbon. But how do you balance...

Who and when first time introduced below equations(dont have to be in same notation, content is important)? If this formula is always the same, what is contribution of Navier, what of Stokes, what changes all these years?

For this problem, The solution is, However, I have a question about the solution. Does someone please know why they write out ##\frac{dF}{dx} = \frac{\partial F}{\partial y}y' + \frac{\partial F}{\partial y'}y''## since we already know that ##\frac{dF}{dx} = 0##? Thanks!

$$(b-a)^2-4(b-c)(c-a)=0$$ $$b^2-2ab+a^2=4(bc-ab-c^2+ac)$$ $$b^2-2ab+a^2+4ab=4bc-4c^2+4ac$$ $$(b+a)^2-4ac=4c(b-c)$$ $$b-c=\frac{(b+a)^2-4ac}{4c}$$ I don't know how to continue and not even sure what I did is useful. Thanks

Hi; given the equation ydy/dx=x^2 how is the chain rule applied to result in ydy =x^2dx? Thanks

I have having trouble understanding Maxwell's Equations. Can anyone recommend some good book or website that can help me to understand these Equations? How can electric and magnetic fields travel perpendicular to each other? What causes electromagnetic waves to first radiate from its source? I...