Constants Definition and 458 Threads

From my understanding, you can equate ψ1(x) and ψ2(x) at the boundary of x = a, so I plugged in the values of a into x for both equations and I got ψ1(x) = 0 and ψ2(x) = ## (a-d)^2-c ##. I am a bit stuck on where to go from here.

We know that in the universe we can establish an equivalence between length and time through a constant (the speed of light): l = ct and talk about length in units of time (light-years). But, by playing mathematically with the dimensions of M, L and T and the constants G and c we can see...

75 = (1.5 x 10^-3)a + (1.5 x 10^-3)b 105 = (3 x 10^-3)a + (3 x 10^-3)b

I once read (though I don’t remember where) that in the same way that you talk about a dimensionless ratio between Y and X in ordinary space, you can conceive of c as a dimensionless ratio between T and X in spacetime. Do you know where I can find a reliable treatment of that idea? As...

I have wrote all feilds and potentials and I want to find the constants. My first question is " when we say in the a<x<2a the potential is V(x)" then the potential in the a is V(a) or V(0) ( cause it is 0 in our new area) ? Second one is " when I want to write the gausses law for the point x=a I...

I've learned that some cosmological observations do not match with theoretical predictions leading to the hypothesis of dark matter or dark energy. Do you know references which discuss if instead the explanation could be that physical constants slowly vary in space? This seems conceptually...

Proof: Observe that \begin{align*} &li(x)=\int_{2}^{x}\frac{dt}{\log t}\\ &=[\frac{t}{\log t}]_{2}^{x}-\int_{2}^{x}t(\frac{1}{\log t})'dt\\ &=\frac{x}{\log x}-\frac{2}{\log 2}-\int_{2}^{x}t(-\frac{1}{t\log^2 t})dt\\ &=\frac{x}{\log x}+\int_{2}^{x}\frac{dt}{\log^2 t}-\frac{2}{\log 2}\\...

When calculating calories of a food.. It is sort of well known that carbs have 4 cal/gram, protein has 4 cal/gram and fat has 9 cal/gram. I wanted to do an experiment to determine these constants 4,4,and 9 I looked at soup, peanut butter, and a protein mix to get the values from the labels per...

Hello, couple of questions about bubble universes and the physical constants. I understand in an eternal inflation scenario universes bubble off the original during the inflation phase. Firstly, according to this theory, does the new universe creation only happen at an early inflation phase of a...

Ever made a simple model that fits a quadratic function? Tweaking the a, b and c constants to fit new observed data is a bit of a pain. When I was a grad. student I came up with the following simple quadratic rearrangement that uses the intercept (Yo) and the values of x and y that define the...

Hi, I have a value ##100 \pm 0.1## and a function ##\frac{V}{E} = \frac{1}{\sqrt{1 + (\omega r c)^2}}## and I would like to find the uncertainty. Where r = 1000 and c = ##5 \cdot 10^{-8}## are constants. However, I'm not sure to understand how. Here's what I think and did. Since I multiply the...

If we have system of 3 ordinary differential equation in mechanics and we have two initial condition ##\vec{r}(t=0)=0## and ##\vec{v}(t=0)=\vec{v}_0 \vec{i}##. If we somehow get \frac{d^2v_x}{dt^2}=-\omega^2v_x then v_x(t)=A\sin(\omega t)+B\cos(\omega t) Two integration constants and one initial...

Hi, I have some soft body equations that require first order elasticity constants. Just trying to figure out the proper indexing. From Finite Elements of Nonlinear Continua by J.T. Oden, the elastic constants I am trying to obtain are the first order, circled below: My particular constitutive...

I was wondering how they measured or calculated these differences? I don't know what they refer to, but assume theyre scattering Hydrogen with Tritium or Deuterium to measure the difference of something. https://physics.nist.gov/cgi-bin/cuu/Results?search_for=shielding+difference

We have a scalar potential $$\Phi(\vec{r})=\frac{q}{4\pi\epsilon_0} \left( \frac{1}{r} - \frac{a^2\gamma e^{-\gamma t}\cos\theta}{r^3}\right)$$ and a vector potential $$\vec{A}(\vec{r})=\frac{a^2qe^{-\gamma t}}{4\pi\epsilon_0r^4}\left(3\cos\theta\hat{r} + \sin\theta\hat{\theta} \right) .$$ how...

Q) I have to explain the relationships between system constants for a perfect gas. Hi can somebody explain this to me. I am kind of confused what this means and where to start and what to do. Also not 100% sure what a perfect gas is.

see attached image, it asks to repesent it in x-graph constant "a" isn't conditioned. Do I need to separate it into a few cases of the constant a and represent each in one x-graph?

[Moderator's note: Spin off from another thread due to topic change.] This is a weird argument to me. We can define metric units, but pretty much everything is defined by something else that we measure. Certainly their are unitless scalar "constants", but they are still basically defined by...

I am not getting any ideas to solve this without the universal constants. The method that I want to use invloves the speed of light, which is a universal constant.

1/2 kx^2 = mgh

If Planck constant h and light speed constant c were (very) different, would we notice it? (I know we can change units and make h and c take any numerical value we like. But let‘s stick with one set of units.) I assume rulers, clocks, coupling constants, all dimensionless constants would...

Does it not raise question to be able to build two parameters with the same dimension and order of magnitude of two fundamental constants from five parameters (other fundamental constants and measured properties)? $$\sqrt{10\frac{\left(\varepsilon_0 e^{-2}\right)^3\left(k_B T\right)^4}{\rho_c}}...

The previous part was to show that ##a_+ \psi_n = i\sqrt{(n+1)\hbar \omega} \psi_{n+1}##, which I just did by looking at$$\int |a_+ \psi_n|^2 dx = \int \psi_n^* (a_{-} a_+ \psi_n) dx = E+\frac{1}{2}\hbar \omega = \hbar \omega(n+1)$$so the constant of proportionality between ##a_+ \psi_n## and...

Can we explain the cosmological constant in this way ? The Einstein tensor is derived from the Ricci tensor and one property is that, like the stress-energy tensor, its covariant derivative shall vanish. Since the covariant derivative of the metric vanishes it can be added to the EFE as...

##4x^4+Ax^2+11x+b##≡##(x^2-x+2)(ax^2+mx+d)## ≡##ax^4+(m-a)x^3+(d-m+2a)x^2+(2m-d)x+2d## ##a=4## ##m-a=0, m=4## ##d-m+2a=A## ##2m-d=11## ##2d=b## ##A=1##, ## B=-6 ## is that correct?

So are my constants a=-1/4, b=0, c=3, and d=0?

During an experiment, using Hooks law resulted in a spring constant of 7,8N/m while for the oscillation-method the constant was 8,6N/m. Could someone help me to clarify whay they differ and which vlsue is the correct one.

Hey there! I am still rather new to renormalising QFT, still using the cut-off scheme with counterterms, and have only looked at the φ^4 model to one loop order. In that model, we renormalise with a counterterm to the one-loop four-point 1PI diagram at a certain energy scale. Do I simply, in...

I have just started out with ODE's and in none of the general form in the classification have I seen a term with no variable but some questions do have constants in the exercise. I am just confused as to why are they not in general forms. Are they redundant? Do they not contribute anything to...

When designing a panel, it is imperative that you keep the components inside at a temperature which they can operate optimally at; allowing the air temperature to go above this limit can cause component failure and fire. To assist with calculating the air flow required to keep the components...

I do not understand the following sentence (particularly, the concept of extra symmetry): 'If all ##\alpha^i## are the same, then there is extra symmetry and corresponding constants of motion'. OK so let's find the Lagrangian; we know it has to have the form: $$L(q, \dot q) = T(q, \dot q) -...

Hello, I am writing a blog post about Physics Constant. I recently found out how you can find out the Constant of Proportionality. and had an idea that all the Physics Constants were Constants of Proportionality. but I have no idea how to confirm this because there are so many. so I don't know...

I am heavily confused about the coupling constants. I primarily refer to this source https://www.physicsmasterclasses.org/exercises/keyhole/en/projects/running_alphas.html , but other sources were not able to lift my confusion either. First, in the figure, the scales appear as quite failed. The...

I'm having a hard time grasping the concept of reducing the two recursive relations at the end of the frobenius method. For example, 2xy''+y'+y=0 after going through all the math i get y1(x) = C1[1-x+1/6*x^2-1/90*x^3+...] y2(x) = C2x^1/2[1-1/3*x+1/30*x^2-1/630*x^3+...] I know those are right...

I can see why it would be pretty illogical to speculate that physical constants change over time, but is there more to it than just being 'illogical' to assume otherwise? Is it axiomatic in physics to presume certain physical constants are constant, because otherwise stuff like atoms and things...

EQ 1: Ψ(x,0)= Ae-x2/a2 A. Find Ψ(x,0) So I normalized Ψ(x,0) by squaring the function, set it equal to 1 and getting an A I. A=(2/π)¼ (1/√a) B. To find Ψ(x,t) EQ:2 Ψ(x,t)= 1/(√2π) ∫ ∅(k) ei(kx-ωt)dk --------->when ω=(ħk2)/2m and integral from -∞ to +∞ EQ 3: ∅(k)= 1/(√2π) ∫ Ψ(x,0)...

The set of quantum numbers for the 4p orbital is: 4, 1, {-1,1}, +-1/2 (n,l,m,s) The set of quantum numbers for the 4d orbital: 4,2,{-2,2},+-1/2 Hence we can calculate DeltaE for the 4p sub levels for j=1+- 1/2 And for the 4d sub levels as j=2+-1/2. Giving four total values for Delta E as: C_4p...

NO TEMPLATE, MISPLACED HOMEWORK Summary: What are the values of constants in power-law fluid relation when the fluid behaves as an ideal fluid, a Newtonian fluid and a non-Newtonian fluid? τ = A(du/dy)^n +B Where A, B and n are constants that depend upon the type of fluid and conditions...

I do not know what I'm doing wrong but I'm working on the problem of finding the normalization constants for the energy eigenstate equation for a 1D plane wave that is traveling from the left into a potential barrier where E < V at the barrier. This is from Allan Adams' Lecture 12 of his 2013...

what are lame's constants for material? their definitions? their proof "if exist"?

Were the universal physical constants already in place at the instant of the BB? Things like Planck's constant, the speed of light, the various mass of particles, the various force values. Was it possible that the early universe ( the first couple of billionths of a second or so) existed without...

I can measure O2, Co2, TGP, and temperature, Want to calculate the rest gases, so N2, and Ar in my water. There for i bulit up an axcel table. So i get to the point to calculate Bunsen contans on different Temperature. I have this calculation: ln(β)=exp(A1 + A2*(T/100) + A3*ln(T/100) +...

I don’t understand how the second (-2) (in front of the integral sign) gets into the equation. Can you please help me?

I’d like to know if anyone has formulas for calculating the spring constant (k) of coil springs, from their physical dimensions. I bought a coil spring, suspended a 0.6 kg mass to it, observed its oscillation period at very close to 0.6 seconds, and so believed the spring constant “k” to be...

Hi all, I am sure I am missing something really elementary, but I would really appreciate someone pointing it out to me. So, if we consider the situation in abelian gauge symmetry, say for fermion matter ψ, of charge q. The transformation law for ψ is, ψ→ψ' = e[- i q θ(x)] ψ. We then have to...

Hi, This is a general question: Do the motor constants KV and KT stay constant at high current? Thanks

Homework Statement 2Fe(s) + 3Cl2(g) ⇔ 2FeCl3(s)[/B] Keq = 53.25 [CL2(g)] = ?M Answer = [0.2658M] Homework Equations Keq = (cC)(dD)/(aA)(bB) The Attempt at a Solution Keq = [Cl2]3 53.25 = (Cl2)3 I’m confused because I feel like I need more to work with in this question. It seems like I...

Hello! (Wave) Let $m$ be a natural number. I want to check the sequence $\left( \binom{n}{m} n^{-m}\right)$ as for the convergence and I want to show that there exist constants $C_1>0, C_2>0$ (independent of $n$) and a positive integer $n_0$ such that $C_1 n^m \leq \binom{n}{m} \leq C_2 n^m$...

Homework Statement a) Consider 2 springs, connected in series. If they have different spring constants k1 and k2 then what is the effective spring constant for the double spring system? Give a convincing argument for your formula. You may assume that the mass of the springs is negligible. b)...