Yes the mistake is in the exponent##(e^{3i\pi}+e^{\frac{\pi}{3}})##. It's ##(e^{3i\pi}+e^{\frac{i\pi}{3}})##.
I just plugged ##\sqrt[3\,]{e^{\frac {2i\pi}{3}}} +\sqrt[3\,]{-\sqrt 3 e^{i\pi/6}}= 3^{1/6} e^{-5i\pi/18}+e^{\frac {4i\pi}{18}}## into ##\sqrt[3\,]...
##(-\frac 32 - i \frac{\sqrt 3}{2})^{1/3}= \sqrt[3\,] {e^{3i\pi}-e^{\frac{\pi}{3}}}## and ##(-1)^{2\over 9}=\sqrt[3\,] {e^{3i\pi}+e^{\frac{\pi}{3}}}##
When trying to solve ##(-3/2 - \frac{i}{2} \sqrt{3})=(a+bi)^3## I get ##a(a^2-b-2b^2)=\frac{3}{2}## and ##b(2a^2+a-b^2)=\frac{\sqrt{3}}{2}##.
How...
I don't know how to start with the factorization.
$$\frac{(-1)^{2/9} + (-3/2 - \frac{i}{2} \sqrt{3})^{(1/3)}}{(-1)^{2/9}- (-3/2 - \frac{i}{2} \sqrt{3})^{(1/3)}}$$
Any hints would be nice. Thank you.
"The group can, however, be given a different topology, in which the distance between two points is defined as the length of the shortest path in the group joining to "
What does this give us in formal math ?
I'm a bit lost, is ##[0,2\pi]-(\mathbb{Q}\cap [0,2\pi])## equal to H or ##\mathbb{P}## ?I've never worked with topological groups,how does a disconnected topological group or set become connected?
"The group given by ## H = \left\{ \left( \begin{array} { c c } { e ^ { 2 \pi i \theta } } & { 0 } \\ { 0 } & { e ^ { 2 \pi i a \theta } } \end{array} \right) | \theta \in \mathbb { R } \right\} \subset \mathbb { T } ^ { 2 } = \left\{ \left( \begin{array} { c c } { e ^ { 2 \pi i \theta } } & { 0...
I am failing to understand the way to get this answer . Is there a simple computation or property that easily gives this answer ? I tried the formula for ##v_x(Q)## without success.
We have a sample of X, a Normalized Gaussian random variable.We divide the data into positive and negative.
Each will have a conditional variance of ## 1−\frac{2}{π}## .
Can someone show how to get this result ?
I found this problem here (page 3) ...
Since δ##T_V## is a function of T and P there should be a way to change variables P and T in the formula for ##\delta T_S## and express it as a function of only δ##T_V## and ##\gamma##.
##\delta P_V =(\frac{\partial P}{\partial T} )_V \delta T_V =\frac{nR}{V}\delta T_V##.
I don't know how to use ##TP^{\frac{1-\gamma }{\gamma}}=cst## to make ##\delta T_S## a function of ##\delta P_V##,T,P and ##\gamma##.
We consider a system composed of liquid helium in equilibrium with its vapor at very low temperature T, each phase being considered extensive. We neglect the mass of the gas compared to that of the liquid, as well as the heat capacities of the gas and the walls compared to that of the liquid...
Indeed,Is ##\Delta S_{th}=\mp\frac{Q}{T_0}=\mp\int_{T_i}^{T_0}\frac{C(T)}{T_0}dT ## correct ?
If so then question b) is ## \Delta S_{univ}=\int_{T_i}^{T_0}C(T)(\frac{1}{T}-\frac{1}{T_0})dT ## when the water heats up and ## \Delta S_{univ}=\int_{T_i}^{T_0}C(T)(\frac{1}{T_0}-\frac{1}{T})dT ##...
for a)##\Delta S=\mp \int_{T_i}^{T_0}\frac{C(T)}{T}dT## and ##\Delta S_{th}=\int_{T_i}^{T_0}\frac{dQ}{T_0}dT## so ##S_{univ}=\Delta S_{th}+\Delta S##.
What is ##dQ## equal to ? I don't know how to answer question b).
Thank you for your help.
Hello,
I am having trouble understanding the two friction force terms from the ball rolling on page 4 of this physical model: http://www.dewtronics.com/tutorials/roulette/documents/Roulette_Physik.pdf
What is the reason for the cos\theta term ?
I think the frame of reference is made up of the...
Hello,
The state | W \rangle = \frac { 1 } { \sqrt { 3 } } ( | 001 \rangle + | 010 \rangle + | 100 \rangle ) is entangled.
The Schmidt decomposition is :
What would the Schmidt decomposition be for | W \rangle ?
I am also intersted in writing the reduced density matrix but I need the basis...
Hello
1. Homework Statement
The dipole moment of an ammonia molecule is ##d_0=5*10^{-30} C.m##.If we apply a static electric field of ##\mathcal { E }=1*10^{6 }V*m^{-1}## to an ammonia molecule initially in the state ## |ψG⟩## where the nitrogen molecule is considered to be on the left,we make...
I think I have an explanation :
The generator gives the system {resitance,capacitor} the electric energy :
The capacitor charges itself by en absorbing half ( the work ##W=\int vdq##). The difference represents the lost energy through the Joule effect :
This energy is received...
I want to know how to express the entropy change , I think the entropy change of the universe is 0 but I'm not sure what the equation is.The RC circuit is getting heat from the reservoir and work from the generator,I'm guessing it's to make it a reversible process.
Hello,I would like some help for a problem
Homework Statement
Initially:At t=0 [/B]the cylindrical capacitor of capacitance c=\frac{\epsilon s}{d} (d the distance between the 2 electrodes and s their surface; \epsilon = \epsilon(T) is the dielectric permittivity) is discharged and we close the...
Mentor note: Thread moved from the Technical Math section, so there is no template.
@yamata1, , in the future, please post homework problems or exercises in the Homework & Coursework sections, not in the Technical Math sections. I have moved your post.
Hello,
I would like some help with an...
Thank you for your explanations.The same test asked what the wavelength of the photon emmited for the transition between first and second excited states of the hydrogen atom was.The choices were :
##a##- < 652 nm
##b##- >652 nm
##c##- equal to 652 nm
##d##- >241 nm
##e##- equal to 241nm
The...
since ##J_z|j,m>=m|j,m>## and ##J^2|j,m>=j(j+1)|j,m>## regardless of ##m## we still don't have ##j## ,it cannot be enough to determine a one-dimensional subspace of the state space ?