Constant Definition and 1000 Threads

While separating variables in the Schrodinger Equation for hydrogen atom, why are we taking separation constant to be l(l+1) instead of just l^2 or -l^2, is it just to make the angular equation in the form of Associated Legendre Equation or is there a deeper meaning to it?

I keep hearing that the relative speed of light remains constant because time and lengths change with speed, what I believe is called the Lorentz factor. At slow speeds the Lorentz factor is extremely small, so what do people believe accounts for the rest of the change? If I travel...

Homework Statement An object moves at constant speed in a circular path. True statements about the motion include which of the following? a) the velocity is constant b) the acceleration is constant c) the net force on the obj is 0 since its speed is constant Homework Equations hm none...

Homework Statement Show that if the Lagrangian does not explicitly depend on time that the Hamiltonian is a constant of motion. Homework Equations see below The Attempt at a Solution method attached here: Apologies this is probably a bad question, but just on going from the line ##dH## to...

In the last years a discrepancy between two methods to measure the Hubble constant appeared. Measurements based on redshift and the cosmic distance ladder produced results of about 73 km/(s*Mpc) while measurements based on the cosmic microwave background lead to results of about 68 km/(s*Mpc)...

Homework Statement One mole of pure ethyl alcohol was treated with one mol of pure acetic acid at 25 °C.One third of acid changes into ester at equilibrium The equilibrium constant for the reaction will be Homework Equations C2H5OH+CH3COOH------>C2H5COOCH3[/B] K={A}^m{B}n/{C}^x{D}^z where...

Why is the accelerating expansion of the universe not explained simply by the perspective of acceleration caused by a constant (non accelerating) universal expansion? Let's take two particles (X,Y) in a 1d expanding universe where it expands universally by 1 unit per per unit time. O represents...

Homework Statement Light of free-space wavelength λ0 = 0.87 μm is guided by a thin planar film of thickness d = 3.0 μm and refractive index n1 = 1.6, surrounded by a medium of refractive index n2 = 1.4 critical angle = 61.04° n0 = 1.00 (a) Determine (i) the angle of incidence θ and (ii) the...

Homework Statement Is the least count constant for Vernier scale like 0.1 mm or variables? 2. The attempt at a solution If the main scale readings are 10 mm and the vernier scale readings are 9 mm, the least count is MSD/VSD = 9/10 = 0.9 So the least count is 0.1 mm for every count in the...

Hello! If you have a Lagrangian (say of a scalar field) depending only on the field and its first derivative and you want to calculate the ground state configuration, is it necessary a constant value? I read about Spontaneous symmetry breaking having this Lagrangian $$L= \frac{1}{2}(\partial_\mu...

Homework Statement For the equation y=cx[L−x] say for a circle with the value of L at 100 meters and the value of x at 25 meters. What would be the value of the constant c for a perfect circle. 3. Attempt at the Solution: I can approximate and graph this with different values of c however I'm...

Homework Statement Let ##S,T \subseteq \mathbb{F}## be nonempty sets. Assume ##\sup (S)## and ##\sup (T)## both exist in ##\mathbb{F}##. Show that ##\forall a \in \mathbb{F}^+ \cup \{0\}## we have ##\sup(aS) = a \cdot \sup (S)##. Homework EquationsThe Attempt at a Solution First I prove the...

Homework Statement This problem is taken from Problem 2.3, Introduction to Vibration and Waves, by H.J. Pain and P. Rankin: A critically mechanical system consisting of a pan hanging from a spring with a damping. What is the value of damping force r if a mass extends the spring by 10cm without...

Motion in a straight line has three formulas 1. v = u + at 2. v^2 - u^2 = 2as 3. s = ut + 1/2 at^2 These three formulas are applicable when a is constant. Now my question is 'what does it mean by 'when a is constant'? Could you please explain it?

Hi, I am trying to wrap my brain around special relativity equations but I'm struggling with the math. I am a computer programmer comfortable with the algebra and but never studied calculus or physics. Say I am already traveling at velocity "v" where "v" is approaching the speed of light. I...

From this link https://en.wikipedia.org/wiki/Baryon_acoustic_oscillations#Measured_observables_of_dark_energy , I can't get this relation : ##c\Delta z = H(z)\Delta \chi\quad\quad(1)## with ##z## redshift, ##H(z)## Hubble constant at redshift = ##z## and ##\chi## radial coordinates. One...

This year alone we have conflicting speeds for the Hubble Constant with 67.66 (+ or - 0.42) from the Planck Mission and 73.45 (+ or - 1.66) from the Hubble Space Telescope. The answer is simply found, and is between those figures. The furthest thing we can see (in theory) is 13.8 billion light...

I've noticed that a very easy way to generate the Lorentz transformation is to draw Cartesian coordinate axes in a plane, label then ix and ct, rotate them clockwise some angle \theta producing axes ix' and ct', use the simple rotation transformation to produce ix' and ct', then just divide...

Hello, According to the following equation describing the effective Hamaker constant of two identical bodies immersed in a liquid : AALA = (AA1/2 - AL1/2)2, for high values of AL, the effective attraction of the A-like media is larger than in vacuum. How is this possible physically ?

Homework Statement Discussions of the possibility of a tangential E-field external to a current-carrying conductor must include a voltage source and a return path. Here the problem is reduced to (we believe) the simplest possible geometry. Assume that a circular conducting loop has constant...

Homework Statement The figure below shows the hyperfine structure in the transition 6s $^2S_{1/2}$ - 8p $^2P_{3/2}$ in 115In (I = 9/2). The measurement is made using a narrow-band tunable laser and a collimated atomic beam; hence the Doppler width is greatly reduced. The 6 components shown have...

Depending on the answer to this question, I may have others. Consider a one-dimensional ice rink. Rightwards is taken as the +x direction. A box of mass m slides leftward on the surface with a constant velocity v. Two people go to opposite ends of the box and apply equal and opposing forces...

So enthalpy is the heat content of a system at constant pressure. Enthalpy change is equal to the heat absorbed or evolved by the system at constant pressure. If my understanding is correct, a system whose temperature goes up will return back to that starting temperature if pressure is kept...

Suppose a comet F ,at 1 AU distance, is traveling toward a massive body (a neutron star or other) with v= .99 c, suppose also that a = 3 km/s^2 and (to simplify calcs) that it is uniform from there to the star. It will hit the star after ca. 1000 seconds and its speed should equal C: 297*10^9...

Why is the speed of light a constant?

Homework Statement A parallel plate capacitor has a capacitance of 7.8 μF when filled with a dielectric. The area of each plate is 1.5 m^2 and the separation between the plates is 1.3 x 10-5 m. What is the dielectric constant of the dielectric? Homework Equations C= (K(8.85E-12)A)/d The...

Hello. I have an equation which I understand partially but after understanding the purpose of coefficients in the below equation I think my understanding will enhance. * I found it on: https://www.desmos.com/calculator/dnzfajfpym What decides that I need coefficients for x2 in the given...

Hello. In fields and waves and transmission lines We have a attenuation constant formula with power relations: 1- Alpha = 1/2R0(R+G|Z0|^2) 2-Also we can calculate attenuation constant from these : Z0= radical[(R+jwL) / (G+jwc)] gamma = radical[(R+jwL)(G+jwc)] I want show alpha from 1...

This Forbes article written by Ethan Siegel talks about the expanding universe and the Hubble constant that isn’t so constant. Surprise! The Hubble Constant Changes Over Time https://www.forbes.com/sites/startswithabang/2018/06/29/surprise-the-hubble-constant-changes-over-time/

This is not a school problem, just my own mucking about, but since it has the form of a problem, I am willing to shift it to the "homework problems" rubric. If there is a theoretical string (no thickness, etc.) that is non-stretchable tied to two endpoints and is long enough to be able to form a...

Allegedly, string theory (in it's simplest form) predicts that cosmological constant must be negative (or zero). Can someone explain where does this result come from? A reference would also be welcome.

The question is stated as the following: When a 3.60 kg object is placed on top of a vertical spring, the spring compresses a distance of 2.83 cm. What is the force constant of the spring? The correct answer was acquired by using the equation F = mg = -kx, where k is the spring constant and x...

Homework Statement Homework Equations Is my solution correct? If not then please point out the mistakes and help me solve this question in the right way. Thanks in advance. The Attempt at a Solution

Show that ##\int_{0}^{\infty} e^{-x}ln(x)\,dx = -\gamma ## when ##\gamma## is Euler–Mascheroni constant My solution is ... ## u = ln(x) ## and ## du = \frac{dx}{x}## ## dv = e^{-x} dx## and ## v = -e^{-x}## so... ##\int_{0}^{\infty} e^{-x}ln(x)\,dx =...

Why \int_{0}^{\infty} e^{-x}ln(x)\,dx = -\gamma when \gamma is Euler–Mascheroni constant My solution is ... u = ln(x) and du = \frac{dx}{x} dv = e^{-x} dx and v = -e^{-x} so... \int_{0}^{\infty} e^{-x}ln(x)\,dx = -ln(x)e^{-x}+\int_{0}^{\infty}\frac{e^{-x}}{x} \,dx when...

Was watching some documentaries and got confused about something. People say that Einstein unintentionally predicted that the universe was expanding, and that he inserted the cosmological constant to represent a force pulling it back in. But other sources seem to imply that the universe was...

Homework Statement Homework EquationsThe Attempt at a Solution (a) Total energy is $$E=\frac{-e^2}{4\pi\epsilon_{0}R}-\frac{B}{R^{5/6}}$$ Taking derivative of E with respect to R and equating it to zero when R=R0 yields, i.e, $$\frac{dE}{dR}{\bigg|}_{R=R_0}=0$$ when R=R0 yields...

I have seen how to solve the heat equation: $$ \frac{ \partial^2 u(x,t) }{\partial x^2} = k^2 \frac{ \partial u(x,t) }{\partial t} $$ With boundary conditions. I use separation variables to find the result, but i don't know how to solve the equation plus a...

Hello, I have a question regarding Damped Harmonic Motion and I was wondering if anyone out there could help me out? Under normal conditions, gravity will not have an affect on a damped spring oscillator that goes up and down. Gravity will just change the offset, and the normal force equation...

I know that the following two functions have the same derivative: ##\arctan (x-1)## and ##2 \arctan (x-1 + \sqrt{(x-1)^2+1})##. Out of curiosity, how can I find the constant value at which they differ? I tried to add ##\pi / 2## to arctan(x-1) but I'm not sure if that works or not...

Greetings! I've been brushing up on some thermodynamics recently and came across a perplexing sentence in my notes and text from undergrad. It says that for a combustion reaction, such as the combustion of heptane: C7H16 (l) + 11O2 (g) ---> 7CO2 (g) + 8H2O (l) That this process carried out at...

Hi all I have struggled with the assumptions that the speed of light is absolute and constant. I have some logic to this which is based on the common assumptions that light behaves both as a wave and a particle. It is also based on light having mass, the effects of heat and vacuum environments...

Hi, I want to be sure i understand correctly the implications of problem 2 in: http://universeinproblems.com/index.php/Time-dependent_Cosmological_Constant "when G is constant, Lambda is also a constant if and only if the ordinary energy-momentum tensor Tμν is also conserved " As far as i...

so i have been trying to calculate boltsmann constant by assuming the fact that for an ideal gas the equation : PV=nRT is true. i assume that for containing each molecule the wall needs to apply a force. now here is where it get's a little weird. each molocule should be only deflected in the...

The way I have understood it is that dynamic torque involves angular acceleration, while static torque has zero angular acceleration: α =Δω/Δt = 0 But static torque still has centripetal acceleration with constant speed: ac = v2/r where v is linear velocity, and r is the radius Then F = mac...

A quantity of ideal gas undergoes an expansion that doubles its volume. Does the gas do more work on its surroundings if the expansion is at constant pressure or at constant temperature? The answer in the book says W at constant temperature gives a greater value for the given case. But when I...

Homework Statement I was going through this PDF to review for my AP Physics C E&M exam: https://apcentral.collegeboard.org/...course=ap-physics-c-electricity-and-magnetism I was also watching this video (which discusses the solutions): I am stuck on part 2(b) (page 7 of the PDF, 17:18...

Hi PF! I'm trying to solve an ODE through the Ritz method, which is to say approximate the solution through a series $$\Phi = \sum_{i=1}^N a_if_i,\\ f_i = \phi_i-d_i.$$ Here ##a_i## are constants to be determined and ##f_i## are prescribed functions, where ##\phi_i## is a function and ##d_i##...

Links for context: 1. https://en.wikipedia.org/wiki/Yukawa_potential 2. https://en.wikipedia.org/wiki/Yukawa_interaction#Classical_potential I'm working on my BSc right now and I'm solving the energies of 2 nucleon systems (so basically just deuteron) by treating them as non-relativistic two...

Homework Statement In the circuit shown S is closed at t = 0 . Find the time constant (in s) if C = 2μF. Homework Equations τ = Req C The Attempt at a Solution R = ##\frac{10*10}{10+10}## R = 5MΩ τ = 5*106 * 2*10-6 = 10 s Could somebody check my answer?