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  1. Dopplershift

    Other Entering a PhD Physics Program While Teaching High School?

    Hello, I am currently a high school physics teacher in Chicago. I am thinking about going back to school to get a PHD in Physics. I currently have a B.S. in Applied Physics and a secondary education license. I would like to find a way to go back and get a PHD. I cannot afford to quit my job...
  2. Dopplershift

    I Understanding Continuous Variable QKD

    So, I am doing my undergraduate research project in Quantum Cryptography, and I have some confusion in a few areas, especially in the topic of continuous variable quantum key distribution. From what I understand, Discrete Variable - Single photon. That is, for example, the BB84 protocol. Bob...
  3. Dopplershift

    Rocket's Initial Mass

    I'm confused, how is the initial velocity zero? It says that the fuel gives us a v0 of 3.0*105? The problem is when I plug in the values of the conditions into my final equation, (equation 2).
  4. Dopplershift

    Rocket's Initial Mass

    The problem states: Typical chemical fuels yield exhaust speeds of the order of 103 m/s. Let us imagine we had a fuel that gives v0 = 3 × 105 m/s. What initial mass of fuel would the rocket need in order to attain a final velocity of 0.1c for a final mass of 1 ton? I derived the equation in the...
  5. Dopplershift

    Find Hamiltonian given Force

    Homework Statement A particle with mass, m, is subject to an attractive force. \begin{equation} \vec{F}(r,t) = \hat{e}_r \frac{k}{r^2}e^{-\beta t} \end{equation} Find the Hamitonian of the particle Homework Equations H = T + U Where T is the kinetic energy and U is the potential...
  6. Dopplershift

    Limits of Integration of a Triangle

    That makes sense. Thank you! :)
  7. Dopplershift

    Limits of Integration of a Triangle

    You didn't misunderstood, I mistyped, my apologies. It is dZ. My limits I assumed are 0<y<1 0<x< y
  8. Dopplershift

    Limits of Integration of a Triangle

    How to I integrate if the integral is a sum such as dz = y dx + (x+2y)dy ? And are my limits of integration correct?
  9. Dopplershift

    Limits of Integration of a Triangle

    Homework Statement Suppose you have a Triangle with the vertices, (0,0) (1,1) and (0,1). Integrating along that path. I have some differential function dZ where Z = Z(x,y) Homework Equations The Attempt at a Solution [/B] If I need to integrate, then I need to find the limits of...
  10. Dopplershift

    Need Help With Gradient (Spherical Coordinates)

    So would it be: \begin{equation} \begin{split} f(r) = rcos(\theta) \\ \frac{\partial f}{\partial r} = cos\theta \\ \frac{\partial f}{\partial \theta} = - rsin \theta \\ \frac{\partial f}{\partial \phi} = 0 \end{split} \end{equation} So the gradient is \begin{equation} cos\theta \ \hat{r} +...
  11. Dopplershift

    Need Help With Gradient (Spherical Coordinates)

    if you're asking if I know how to take partial derivatives, then yes. The issue lies in I don't know where to begin since there is ##\hat{r}##, ##\hat{\theta}##, ##\hat{\phi}## in the equation.
  12. Dopplershift

    Need Help With Gradient (Spherical Coordinates)

    Homework Statement Find te gradient of the following function f(r) = rcos(##\theta##) in spherical coordinates. Homework Equations \begin{equation} \nabla f = \frac{\partial f}{\partial r} \hat{r} + (\frac{1}{r}) \frac{\partial f}{\partial \theta} \hat{\theta} + \frac{1}{rsin\theta}...
  13. Dopplershift

    3-D Dirac Delta Function

    Never Mind, I figured it out. I was overthinking the problem. Thanks for your help! :)
  14. Dopplershift

    3-D Dirac Delta Function

    Okay, so I can setup the integral. \begin{equation} \int_v (r^2 - 2\vec{r} \cdot \vec{r}') \delta_x(x-x_0) \delta_y (y-y_0) \delta_z (z-z_0) dx dy dz \end{equation} I guess I'm confused how I plug ##\vec{r}'## into f(##\vec{r}##)
  15. Dopplershift

    F * r = I * alpha?

    F is the tangetial forice r is the radius (in this case the radius of the pulley) I is the moment of inertia (assume the pulley is a soild disk, so I = 1/2mr^2 alpha is the angular acceleration.
  16. Dopplershift

    Kinematics, deriving equations.

    You have the answer in your relevant equations. We say that change in position is the velocity. That is: \begin{equation} v(t) = \frac{\Delta x}{\Delta t} \end{equation} We used this notation in alegebra-based physics because we are taking the difference between two points which is a secant...
  17. Dopplershift

    3-D Dirac Delta Function

    Homework Statement \begin{equation} \int_V (r^2 - \vec{2r} \cdot \vec{r}') \ \delta^3(\vec{r} - \vec{r}') d\tau \end{equation} where: \begin{equation} \vec{r}' = 3\hat{x} + 2\hat{y} + \hat{z} \end{equation} Where d $\tau$ is the volume element, and V is a solid sphere with radius 4, centered...
  18. Dopplershift

    Why did you choose math over physics or vice versa?

    Have you ever taken a mathematical modeling course. The laws of physics apply there when modeling physical applications.
  19. Dopplershift

    B Is Center of Mass a vector or scalar quantity?

    I agree! But that's what makes math and physics so exciting is the discussions that come out of simple questions. Some of the greatest scientific breakthroughs came from simple questions. It's in our nature to try to go in depth as much as possible and to explore the validity of what we believe...
  20. Dopplershift

    Why did you choose math over physics or vice versa?

    I like to think that Physics is math with a story. The two go hand-in-hand. You cannot study math without knowledge of physics and you cannot study physics without math. I chose physics because I was curious on why and how things work in the universe.
  21. Dopplershift

    I Schrodinger's Interpretation of the Wave Function?

    I have yet to study hamiltonian mechanics, but it's in the upcoming semester. I have only studied Newtonian and Lagrangian mechanics in the field of classical mechanics. I will definitely read what I can and come back to the math once I cover it in my class. Thank you!
  22. Dopplershift

    I Schrodinger's Interpretation of the Wave Function?

    So, if I understand correctly. The wave equation was Schrodinger's way of fitting the data of the wavelength of Hydrogen spectrum, but the disagreement was on what the modulus squared represented? In Born's interpretation, he proposed that it was the probability amplitude of an electron's...
  23. Dopplershift

    B Is Center of Mass a vector or scalar quantity?

    A point in 3D space itself is not a vector, but it's displacement from the origin is. The displacement is the magnitude and the component (x,y,z) is the direction. Vectors are displacement from point a to point b. In physics, we often are more concern with the displacement rather than the...
  24. Dopplershift

    B Is Center of Mass a vector or scalar quantity?

    Remember in 2D Kinematics (projectile motion) where you broke the velocity of the object to both the x and y components. Both the components had a magnitude and direction (either the x-direction or the y-direction). The position of the object at any given time had a x component and y component...
  25. Dopplershift

    B Is Center of Mass a vector or scalar quantity?

    A point is any arbitrary position (0,4,6), a vector is the point's displacement relative to another point. a point would just be the displacement from the origin. If you move the origin and the point of your choice equally, the magnitude of the vector does not change. The direction is simply...
  26. Dopplershift

    B Is Center of Mass a vector or scalar quantity?

    The individual coordinates of the position vector, R, of the center of mass can be broken down into its 3d components (X,Y,Z) if each particle has a position (x,y,z) Thus: $$ X = \frac{1}{M} \sum_{\alpha = 1}^N m_\alpha x_\alpha \\ Y = \frac{1}{M} \sum_{\alpha = 1}^N m_\alpha y_\alpha \\ Z =...
  27. Dopplershift

    B Is Center of Mass a vector or scalar quantity?

    Yes, the center of mass is indeed a vector quantity The center of mass is itself a position, thus it requires an exact position which is given by Coordinates x,y,z (if working in Cartesian coordinates). The position vector R of the center of mass is given by: \begin{equation} R =\frac{1}{M}...
  28. Dopplershift

    I Schrodinger's Interpretation of the Wave Function?

    Schrodinger developed his famous wave equation which describes how the quantum state of a system changes over time. But, what was Schrodinger trying to initially prove with his equation?I assume that it has to do with Debrogile's hypothesis. I know from my classes that we use the Schrodinger...
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