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a. ##L_{+}^{\dagger}=(L_x+iL_y)^{\dagger}=L_x-iL_y=L_{-}## b.##[L_{+},L_{-}]=[L_x+iL_y,L_x-iL_y]=(L_x+iL_y)(L_x-iL_y)-(L_x-iL_y)(L_x+iL_y)=## ##=L_x^2-iL_xL_y+iL_yL_x+L_y^2-(L_x^2+iL_xL_y-iL_yL_x-L_y^2)## ##=L_x^2-iL_xL_y+iL_yL_x+L_y^2-L_x^2-iL_xL_y+iL_yL_x+L_y^2##...

So I answered 1 and 2, got: 1. ##\vec(r)(\theta,\phi)=l(sin \theta cos \phi, sin \theta sin \phi, -cos \theta)## 2. ##L=\frac{ml^2 (\dot{\theta}^2+\dot{\phi}^2 sin^2 \theta)}{2}+mglcos \theta## 3. a ##mlsin \theta -mgsin \theta =l^2 \ddot{\theta}## , b. ##ml^2 \ddot{\phi}=0## 4. I know...

Do you mean ##-\frac{\partial H}{\partial \phi}=m(x\dot{y}-y\dot{x})## Where ##x=rsin\theta cos\phi, y=rsin\theta sin\phi##?

3. Find the hamilton equations 4. using 3. prove the the angular momentum in the z axis ##L_z=m(x\dot y-xy\dot)## is preserved. I got in ##3##: How can I prove 4?

Not it is just that my background is in math (done linear algebra 1+2) so I am checking each step form math (and now physics) point of view

I mean here: Why you have ## a, b, -a, b## and not ##a,b,c,d##?

I am maybe confused with the dirac notations, but how did you get to this expression?

Thanks! So mathematically, are we doing a basis change? as how else can we arrive to ##\left| v_1 \right>= \frac{1}{\sqrt{2}} \left| x \right>+\frac{1}{\sqrt{2}}\left| y \right>## And ## \left| v_2 \right>= -\frac{1}{\sqrt{2}}\left| x \right>+\frac{1}{\sqrt{2}} \left| y \right>## Using the...

Thanks, I do not understand the physics the led to the two equations. maybe I will go a step back ##\left| x \right>## and ##\left| y \right>## are the state of the system after a measure is done? The eigenvectors of ##A## are the state of the system before the mesure? So now we are...

Why ##\left| v_1 \right>= \frac{1}{\sqrt{2}} \left| x \right>+\frac{1}{\sqrt{2}}\left| y \right>## And ## \left| v_2 \right>= -\frac{1}{\sqrt{2}}\left| x \right>$+\frac{1}{\sqrt{2}} \left| y \right>## ? We took the dot product of the eigenvalues of ##A##? Did we use the fact that ##\left|...

Summary: Finding state at t=0, energy values and more So this is my first question in quantum mechanics (please understand). 1. So we have a system, and to describe the state of the system we have to measure, A is an hermitian matrix, that each physical measurable quantity has. To find the...

Why is the left hand diode is conducting? the capacitors do not affect the voltage? do not they both charge to the same voltage and the diode is not conducting?

Homework Statement Graph ##V_{out}## Homework EquationsThe Attempt at a Solution When ##V_{in}=V## C1 is positive on the left and negative on the right, and C2 is negative on the the down side and positive on the upper side so there is no Vout?

I have a lot of constant so rather than at ##t=0## the answer says something like slope of about ##\frac{1}{t^2}## and frequency of about ##t^3## how did the get to it?

Homework Statement let there be ##\beta(t+\tau)^{-2}e^{-3}cos(at^{3})## where ##\beta##, ##\tau## and ##a## are constants Homework Equations ##\beta(t+\tau)^{-2}e^{-3}cos(at^{3})## The Attempt at a Solution I know the graph is going up and down exponential but how can I draw it more...