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 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...
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...
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?
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?
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...
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...
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...
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...
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$$.
Since the system does not alter the surroundings, ##\Delta...
Homework Statement
The ends of a stretched wire of length L are fixed at x=0 and x=L. In one experiment, the displacement of the wire is given by ##y=A\sin\left(\frac{\pi x}{L}\right)\sin(\omega t)## and its energy is ##E_1##. In another experiment, the displacement of wire is given by...
oops...
The number of electrons exchanged by 1 mole of thiosulphate is 1.
$$2e^-+2S_2O_3^{2-}\rightarrow S_4O_6^{2-}$$
Hence n-factor is 1 and not 2. Now I got the given answer.
I get it. I can write $$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 $$i(t)=\frac{V(t)}{Z}=\frac{V_0e^{i\omega t}}{R+i\left(\frac{1}{\omega C}-\omega L\right)}$$...