Homework Statement
A Spherical potential which is
0 for 0<r<a
Vo for r>a
Find the condition for bound states, for the radial function with l=0
Plot the result.
The Attempt at a Solution
I have gotten the equation
- tan(ka)=k/lambda
where k is the wavenumber for the wave inside the well...
Homework Statement
An electron is in an applied magnetic field.
This electron is then radiated with microwave radiation which is at the correct larmor frequency.
Homework Equations
1) Does the electron absorb microwave radiation when the applied microwave radiation induces a spin flip...
I think I understand this.
since the overlap of \lambda and the vacuum is zero and also the overlap with the one, two and so one particle functions is zero, \lambda must be zero.
Am I right?
Homework Statement
The problem is to find the eigenkets for the creation operator ,a^{\dagger} if they exist
Homework Equations
a^{\dagger}|\Psi>=\lambda|\Psi>
a^{\dagger}=\frac{1}{\sqrt{2*\hbar*m*\omega}}*(-\hbar*\frac{d}{dx}+m*\omega*x)
The Attempt at a Solution
I use the...
An electron has its spin vector pointing in the positive x-direction and a magnetic field vector is turned on in the positive z-direction.
Question 1. Does the spin vector turn to the positive z-direction and start to precess around the z-axis? Or does is precess around the x-axis...
A beam of particles with spin 1/2 are coming out of a polarizer and moving along the x-axis, the spin of the particles points in the positive y direction. A uniform magnetic field is turned on and off over a short distance compared with the wavelength of the particle beam. The field is given by...
I am trying to solve this Fourier problem where I have to integrate
∫f(x) * exp(-i§x) dx from -∞ to ∞ , where f(x) = exp(-sgn(x))
I tried breaking the function into two pieces where x is from -∞ to 0 and from 0 to ∞ where f(x) would then be exp(x) and exp(-x) and integrating two functions...
There is an example in my textbook which I´m having trouble with.
The example is like this.
"
Find the area of the finite plane region bounded by the four parabolas, y=x^2 , y=2x^2 , x=y^2 , and x=3y^2
The region is called D.
Let u=y/x^2 and v=x/y^2
The the region D corresponds to...
Hi. I have been trying to find the MO diagram for BrF5 since it is not in my textbook. I have been searching the web, and Google but I haven't been able to find anything, if someone knows of a MO diagram on the web I would be thankful If you would tell me where to find it.
I have to find the first three non-zero terms in the Maclaurin series for the function sec(x).
I guess I have to use the known Maclaurin series for cos(x) and doing 1/cos(x) series with long division. I tried that but didn't get anywere close to the right answer. Could anyone please help me?
O.K. I getting close to understanding this. What puzzles me is the last sum. Do you put n+1 so the first term isn't 0? I think I'm missing some information to understand this.
O.K. I see what's going on now, thanks. But I still don't get how to get n+1 from c_k = \sum^k_{r=0} a_r b_{k-r} without doing some multiplication. Please explain to me if you can.
My textbook has an example on multiplication of power series.
" Multiply the geometric series x^n by itself to get a power series for 1/(1-x)^2 for |x|<1 "
from this we get the c_{n}=n+1
O.K. I get that the coefficients are 1 for all n but why +1.
Could someone please explain this to me...
In my textbook there is an example that shows determination whether a series converges or diverges using the limit comparison test.
"
The series is (1+n *ln(n)) / (n^2 + 5)
For n large, we expect an to behave like (n*ln(n))/n^2 = (ln(n))/n, which is greater than 1/n for n>= 3, so we take bn =...
I understand I can't use Pappus's theorem.
So I try to cut the hemispherical shell into horizontal shells up the y axis. Each shell should have the surface 2*Pi*R where R=sqrt(r^2-y^2)
So dS = 2*Pi*R dy
But there is something wrong here, When I integrate from 0 to r I don't get the right...
I have to find the centroid of a hemispherical surface with radius r.
I want to use Pappus's theorem.S=2*Pi*x*s
The surface S, is 2*Pi*r^2 and the length of the curve s, is Pi*r so the distance from the centroid ,which lies on the y-axis by symmetry, to the x-axis is S/(2*Pi*Pi*r) = r/Pi...
Need help with Friedel Crafts alkylation
Hi. In my laboratory textbook there is an explanation on how to make 1,4-Di-t-butyl-2,5-dimethoxybenzene from p-Dimethoxybenzene, tert-butanol and sulfuric acid. I am to put acetic acid and t-butyl alcohol to the p-Dimethoxybenzene. What my textbook...
I am trying to integrate sqrt(1+4*x^2)
I have been trying to rewrite this into sqrt(-4x+(2x + 1)^2) and putting u=2x+1 and substituting but I don't think that makes this any easier. Could someone please give me a hint.
Well I had forgotten all about this problem. I had already figured out the hight of the polar caps. But I have a problem with integrating the caps to find their volumes, could you please give me a hint on that? Berry Boy.
Thanks.
I have to calculate the volume of a sphere of radius 2 that has a hole with radius 1 through the sphere and that includes the center of the sphere. I am trying to solve this by putting semi disk with length 4 units and 1 unit from the base to the top, and then revolving this disk around the line...
Hi. I want to integrate x/(x^2 + ax + a^2)
I tried substitution with u=x^2 then du =2x but that didn't work out neither did the substitution x^2 + ax
I thought of factorizing the denominator and using partial fractions, but I think that's not the way, can't figure out the factorization...
I have a textbook problem I am trying to solve with no luck.
I know 1/(u^2 -1) = 1/2 [ 1/(u-1) - 1/(u+1) ]
I come so far to see that 1/(u^2 -1) = 1/ [(u-1)(u+1) ]
But I don't know what comes next. Could somebody please give me a hint.
I integrated with u=e^x and used partial fraction
to get
-ln(e^x) + 2*ln(e^x -1) +C
I differentiated this back to the beginning, so I should be right. But I got a different looking answer in my textbook.
Hi. I am trying to integrate (e^x +1)/(e^x -1)
I have looked at this for almost an hour and don´t know how to start with it. I want to use substitution but I have to rewrite this in some way. Could anyone please give me a little hint?
Saw this gadget on tv that's supposed to change the taste of wine with a special magnetic field. And the new structure of the wine is to last for 15 days.
Would this be possible at all?
A spherical shell has inner radii a and outer radii b. The temperatures at the inner and outer surfaces are T2 and T1. The thermal conductivity of the shell material is k. I have to derive an equation for the total heat current through the shell.
The equation for heat current through a rod...
O.K. I think I understand this but the real problem I don't understand, here it comes.
An incompressible fluid with density rho is in a horizontal test tube of inner cross-sectional area A. The test tube spins in a horizontal circle with angular speed w. Gravitational forces are negligeble...
The tube accelerates to the right. The water goes to the left, so there must be a force pressing it to the left. I know its not really a force, but It helps thinking of it that way. When you drive a car in a circle your body gets pressed to the sides. Your body is not in a an inertial frame of...