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the particle moves along a ring. so the elemental length should be rdtheta

Homework Statement Normalized equation for particle in a ring, where V=0 on a ring of radius 'a' and infinite everywhere else. Homework Equations The Attempt at a Solution Replcing x by rθ, $$-\frac{\hbar^2}{2I}\frac{\partial^2\psi}{\partial\theta^2}=E\psi$$ By guess, I found out that...

@BvU high probabilty density does not mean high probability. How can you say psi*psi has to be maximum for probability to be maximum?

@BvU I argued this with my professor and so did others in my class. But he told this gives the probability even if it has a dimension.(I couldn't argue more as i trusted his statement becuase his education level is far higher than mine). I even got marks for using the above formula. I used...

A higher psi*psi means a higher probability density. Not a higher probability for different dV. Am I correct? And, After reading some articles, i found that ##4\pi r^2 R^2## (R is the radial wave function) gives the probability.

@haruspex I can't do a dr times the probability density. I need the probability as a function of r and theta. If I just take |R|^2, that will give me the probability density.

Homework Statement The radial wavefunction for ##3d_{z^2}## orbital is $$R=N\sigma^2e^{-\frac{\sigma}{3}}(3\cos^2\theta-1)$$ $$\sigma=\frac{r}{a_0}$$ Find r and θ for which the probabiity of finding the electron is maximum Homework Equations None The Attempt at a Solution ##R^2## gives the...

For example, why isn't F(z,y,z)=f(x)+g(y)+h(z) and only f(x)g(y)h(z)?

@Nugatory I am asking how can one be sure that a function f(x,y,z)=f(x)f(y)f(z)?

In a hydrogen atom, the wave function is written as R(r).Θ(θ).Φ(φ). But how is it separable when the electron is interacting with the nucleus?

Homework Statement For the particle in a box given in the above question, what is the probability of finding the electron between (i) x = 0.49 and 0.51, (ii) x = 0 and 0.020 and (ii) x=0.24 and 0.26 ( x in nm) for both n=1 and n=2. Rationalize your answers. Homework Equations...

@PeroK is it wise to stick with Griffith considering my zero knowledge in linear algebra? Where can I learn linear algebra?

Can you recommend a better book than griffiths? I keep getting more doubts. Like in the equation $$<p>=\int\psi *\frac{h}{2\pi i}\frac{\partial \psi}{\partial x}dx$$ why did griffith choose $$\frac{h}{2\pi i}\frac{\partial}{\partial x}$$ as the momentum operator?

:DD what about this part of the question:

Why does this happen? I mean why does the wave function collapse to an eigenstate after a measurement? What if it was never measured?

I need clarification on this: If the particle was found at C, does it mean there was a psi^2 maxima at/near C?

I am sorry. I don't get you :)

Say a particle was measured to be at a point C. Immediately after this, if i make another measurement, its given in griffith's book that the particle will still be found at C. Isn't this only possible if the particle was at rest?

@BvU i am not asking about de broglie wavelength. I am asking about this

Can you explain this? $$\lambda=\frac{h}{mv}$$

what is delta P? the change in momentum?

the width of central maxima is obtained from ##n\lambda=w\sin\frac{\Delta\theta}{2}## Here, n=1.

Homework Statement An electron is moving in a parallel beam along the x-direction with momentum, p=mv. It encounters a slit of width w. Assuming that the electron gets diffracted somewhere within the central maximum of small angular magnitude Δθ, estimate the uncertainty Δp in its momentum...

How did you get that expression?

This is the course we started with: https://portal.iitb.ac.in/asc/Courses/crsedetail.jsp?ccd=PH%20105

I have already learned those in high school. And the courses given are not for first years. These are the lectures I was given. (these lectures are common for every branch in first year)

they did. at first the prof taught random things from atomic structure. then he discussed light (photoelectric effect, compton effect). Then came blackbody radiation (Rayliegh-jeans law, stefans law, etc) and now we will start quantum mechanics soon. This is my college: http://www.iitb.ac.in/...

My college started physics course with light and blackbody radiation. I am facing difficulties in understanding relativistic energies, Compton effect and specific heats of multi atomic gases. Can you suggest a method for studying modern physics and suggest some good books for getting my concepts...

Homework Statement Using equipartition law, find specific heat of gas containing triatomic linear molecules. Will the result be different if the molecule was non- linear? In what way? Homework Equations According to equipartion theorem, each degree of freedom gets (1/2)kT kinetic energy and...

I have uploaded a page from my prof's lecture on specific heat. Its given that average energy for each vibrational mode is $$\frac{h\nu}{e^{\frac{h\nu}{T}}-1}$$ Hence $$U=(\text{number of vibrational modes)}\times\frac{h\nu}{e^{\frac{h\nu}{T}}-1}$$ In the lecture slide, the number of...

by the object. I think i misunderstood the theorem. A is the fraction of the power absorbed.

According to Kirchoff $$e=J(T,f)A$$ ##e## is the power emitted and ##A## is the power absorbed If ##E## is the power supplied, can I say that $$e=E-A$$

I am not specific about US. The opportunities here in my country is less. I went through the syllabus of aerospace engineering. It seems interesting. What are "those sort of jobs"? @johnnyrev I like fluid mechanics. (I already did a course in fluids in high school and i liked it + I read...

My math part is good. Boeing provides scholarship programs in some colleges here. (http://www.ae.iitkgp.ernet.in/boeing/index.htm [Broken])

I am planning to join an undergraduate course in aerospace engineering. There are not much jobs in my country. I wish to do further studies in other countries (I don't want to stay here). I heard that getting jobs in other countries will be difficult because you need citizenship to work in their...

But Q_surroundings may not always be equal to -Q_system. Should I use ΔS_(surr) + ΔS_(sys) ≥ 0? But that won't give the exact value.

But why:

@ehild that solved the question :D

Homework Statement [/B] Find the power supplied by the battery. Homework Equations $$Z_C=-iX_C$$ $$Z_L=iX_L$$ The Attempt at a Solution $$Z_1=R_1-iX_C=\sqrt{R_1^2+X_C^2}e^{i\phi_1}$$ $$Z_2=R_+iX_L=\sqrt{R_2^2+X_L^2}e^{i\phi_2}$$ $$I_1(t)=\frac{V_0}{\sqrt{R_1^2+X_C^2}}e^{i(\omega...

I have some doubts on entropy change of certain simple process. Can you check if these statements are correct? This is what I know: For a reversible adiabatic process, $$\Delta Q=0$$. $$\Delta S_{system}=\frac{\Delta Q}{T}=0$$. Since the system does not alter the surroundings, ##\Delta...

@Orodruin how can I compute potential energy as a function of time?

Using ##\text{d}K=\frac{1}{2}(\mu \text{d}x) v_y^2## $$K=\frac{1}{4}\mu\omega^2A^2L\cos^2\omega t$$ at ##t=0## $$E_1=\frac{1}{4}\mu\omega^2A^2L$$ $$E_2=\frac{1}{4}\cdot 2\mu\cdot 4\omega^2A^2\frac{L}{2}=4E_1$$

Homework Statement The ends of a stretched wire of length L are fixed at x=0 and x=L. In one experiment, the displacement of the wire is given by ##y=A\sin\left(\frac{\pi x}{L}\right)\sin(\omega t)## and its energy is ##E_1##. In another experiment, the displacement of wire is given by...

oops... The number of electrons exchanged by 1 mole of thiosulphate is 1. $$2e^-+2S_2O_3^{2-}\rightarrow S_4O_6^{2-}$$ Hence n-factor is 1 and not 2. Now I got the given answer.

Homework Statement To a 25ml H2O2 solution, excess acidified solution of potassium iodide is added. The libereated iodine required 20ml of 0.3N sodium thiosulphate solution. Calculate the volume strength of H2O2. Homework Equations Normality = n-factor × Molarity Volume strength = Molarity ×...

@SammyS edited

I get it. I can write $$R+i\left(\omega L-\frac{1}{\omega C}\right)=\sqrt{R^2+\left(\omega L-\frac{1}{\omega C}\right)^2}e^{i\phi}$$ Hence, $$i(t)=\frac{V(t)}{\sqrt{R^2+\left(\omega L-\frac{1}{\omega C}\right)^2}e^{i\phi}}$$ $$i(t)=\frac{V(t)e^{-i\phi}}{\sqrt{R^2+\left(\omega L-\frac{1}{\omega...

In an RLC series circuit let applied EMF be given ##V=V_0\sin\omega t##, $$Z=Z_C+Z_R+Z_L=R+i\left(\frac{1}{\omega C}-\omega L\right)$$ $$|Z|=\sqrt{R^2+\left(\frac{1}{\omega C}-\omega L\right)^2}$$ Then $$i(t)=\frac{V(t)}{Z}=\frac{V_0e^{i\omega t}}{R+i\left(\frac{1}{\omega C}-\omega L\right)}$$...

The loss in energy for A is ##-mgy_A+\frac{1}{2}mv^2## The loss in energy for B is ##\frac{1}{2}mu^2-mgy_B+\frac{1}{2}mv^2##

@haruspex does loss in mechanical energy mean ##\Delta KE ## or the change in the total energy including the potential energy?