# Search results

1. ### Transformation from Cartesian to spherical polar coordinates

Just like to pick up in this old thread, still having trouble with the question. Using what I have already done: δrθ=(∂r/∂x . ∂x/∂θ) + (∂r/∂y . ∂y/∂θ) + (∂r/∂z . ∂z/∂θ) (1) Where: x=r sin θ cos φ and y= r sin θ sin φ z= r cos θ Would (1) then become: δyx= = ((sin...
2. ### Pauli-Lubanski pseudovector

So I have the correct answer, thats great. Thanks for all your help :smile:
3. ### Pauli-Lubanski pseudovector

I understand so you end up with: W2= -(J10P3+J30P1+J31P0) Correct?
4. ### Pauli-Lubanski pseudovector

So using that information and that: ε1234=1 and ε1243=-1 W2= -1/2 (-J10P3+ J30P1+J10P3 +J31P0-J30P1-J31P0) =-1/2 (0)
5. ### Pauli-Lubanski pseudovector

:rofl: Thats what I meant... So M31= - M13 for example...
6. ### Pauli-Lubanski pseudovector

OK so the antisymmetry rule again is: Mab=M-ab
7. ### Pauli-Lubanski pseudovector

OK so the other four terms would be: ε2301 M30P1 ε2310 M31P0 ε2130 M13P0 ε2103 M10P3
8. ### Pauli-Lubanski pseudovector

Ok Im a little confused, could you go into more detail regarding your expansion? Im struggling to see how you got those terms! :confused:
9. ### Pauli-Lubanski pseudovector

Well here is my answer: W2= 0.5 M\mu\nu M\mu\nu P2 + M\mu\rho M\nu\rho P\mu P\nu Where the Pauli-Lubanski pseudovector given was: Wμ= - 0.5 \epsilon\mu\nu\rho\sigma J\nu\rho P\sigma
10. ### Pauli-Lubanski pseudovector

Ive tried the method mentioned in the post below: https://www.physicsforums.com/showthread.php?t=245130
11. ### Pauli-Lubanski pseudovector

Hi can anyone help me prove the result of W2 of the Pauli-Lubanski pseudovector : This is very new to me and I've read I must use terms such as J13 and P3 Where totally antisymmetric symbol is defined by: \epsilon1234=1 and \epsilon1243=-1
12. ### Differential coefficients & metric tensor (Urgent)

Consider a flat 2-dimensional plane. This can be described by standard Cartesian coordinates (x,y). We establish a oblique set of axes labelled p and q. p coincides with x but q is at an angle θ to the x-axis. At any point A has unambiguous co-ordinates (x,y) in the Cartesian system. In...
13. ### Consider the vector Vμ(3,1)

Im told to consider the specific example of the vector: Vμ = (3,1) in the Cartesian coordinates. gμv is the metric tensor Yes I believe they are bases, the question is based around raising and lowering the index in tensors
14. ### Transformation from Cartesian to spherical polar coordinates

Transformation from Cartesian to spherical polar coordinates In dimensions: x=r sinθ cos \varphi and y= r sin θ sin \varphi z=r cos θ Show one example of: ∂z\alpha/ ∂xμ . ∂xμ/ ∂z\alpha = δ\alpha\beta Now here is my answer: δyx=(∂y/∂r . ∂r/∂x) + (∂y/∂θ . ∂θ/∂x) + (∂y/∂\varphi...
15. ### Consider the vector Vμ(3,1)

Using the fact that: gμv= 2x2 identity matrix and the dot product is given by: VμVμ=gμv VμVv Therefore: Vμ=gμvVv So is it correct to say: Vμ= (3,1)
16. ### Consider the vector Vμ(3,1)

Consider the vector Vμ(3,1) Find VμVμ Now here is my attempt Using the following: Vμ=gμvVv I could calculate: Vv=(3,1) But how can I now manipulate this to obtain Vμ
17. ### Basic Probability

Ok Thankyou Ray Vickson just to confirm though the expected number I posted (0.733333) that is correct?
18. ### Basic Probability

Ok so the expected number then would that be 0.733333? But the actual number would of course be one because we cannot have 0.7333 of a faulty TV
19. ### Basic Probability

For the second answer you gave would that figure be obviously 11 x 1/15 = 0.733333 faulty type A TV's. So that would be 1 in every 11 customers gets a faulty brand A TV.
20. ### Basic Probability

Basically Im asked to establish the probability that customer 1 will get a faulty brand A TV. Given that there are 1/3 of TV's in shop are A and probability of faulty TV is 0.2. Hence: 1/3 x 1/5 = 1/15 or 0.06666666 Now the question switches to ask how many faulty brand A TV's will be...
21. ### Basic Probability

So since the probability of a faulty TV for person 1 is 0.06666 or 1/15, after 11 customers the probability would be: 11 x 1/15 =0.733333 Since we cant have 0.7333 of a TV I just round this to 1. Therefore 1 faulty TV after 11 customers.
22. ### Basic Probability

what is the expected number of faulty TV's after 11 customers?
23. ### Basic Probability

Just a quick follow up, what would be the probability for the 11th customer? Would it just be a case of multiplying 0.066666 by 20?
24. ### Basic Probability

Thanks Susskind, think I convinced myself it was too simple:smile:
25. ### Basic Probability

In a shop 1/3 of the TV's are brand A, the probability that a brand A TV is faulty is 0.2. What is the probability person 1 buys a faulty brand A TV? Here's my attempt Im not sure if it seems almost too easy but should I use the rule: P(A) x P(B) = P(AnB) Giving: 0.33333x0.2=0.066666 ??
26. ### Model for single lane of traffic

A model for a single lane of traffic is given by the following pde p dv/dx + v dp/dx + dp/dt = 0 Where: v = kx/p Show that dp/dt = -k Here is my attempt v = kx/p dv/dx = k/p p= kx/v dp/dx = k/v Substituting into original pde: p (k/p) + v(k/v) + dp/dt=0...
27. ### Solve the first order hyperbolic equation

Which equation shall I plug the r value into? Is it: log u = x2/3 + log (2r+4) - r2/3
28. ### Solve the first order hyperbolic equation

So : r = \pmSQRT (x2 -3t) What is the next step?
29. ### Solve the first order hyperbolic equation

So: t = x2 /3 - r2 /3 r2 /3 = x2 /3-t r2 = x2 -3t r = SQRT (x2 -3t)
30. ### Solve the first order hyperbolic equation

So c= log (2r+4) - r2/3 So log u = x2/3 + log (2r+4) - r2/3