Recent content by Physgeek64

But is this not the transformation one makes in lagrangian mechanics to then say ##\frac{\partial L}{\partial \dot{q}} (n \times r) = constant ## by Noether's theorem? Many thanks

Homework Statement How do you show |r_1-r_2| is rotationally invariant Homework EquationsThe Attempt at a Solution So i get that we need to show that it is invariant under the transformations ## r_1 \rightarrow r_1 + \epsilon (n \times r_1)## ## r_2 \rightarrow r_2 + \epsilon (n \times r_2)##...

## \frac{\partial L}{\partial \dot{Q}} = \frac{\partial L}{\partial \dot{q}} \frac{\partial \dot{q}}{\partial \dot{Q}} =\frac{\partial L}{\partial \dot{q}} \frac{1}{1+\dot{K}'} = p \frac{1}{1+\dot{K}'} ## ?? is this along the right lines? Many thanks

Ahh okay then, so I guess i can't make that assumption. In which case i don't know how to proceed, any tips? Thank you, i will change them :)

Homework Statement Given a system with a Lagrangian ##L(q,\dot{q})## and Hamiltonian ##H=H(q,p)## and that the Lagrangian is invariant under the transformation ##q \rightarrow q+ K(q) ## find the generating function, G. Homework EquationsThe Attempt at a Solution ##\delta q = \{ q,G \} =...

But how do i find the result of a measurement. I can show that the expected value is zero, but i don't know what the outcome of an individual measurement would be.

Homework Statement If we have a wave function ##\psi =zf(r)## and we take a measurement of ##L_x## what is the result of the measurement? Homework EquationsThe Attempt at a Solution So i know we can write ##L_x=\frac{1}{2}(L_+ + L_- )## and that ##|\psi > = g(r) |1,0> ## so ##L_x |\psi >=...

So would we say that ##n=m+1## ##\delta_1=2k_1 d## ##\delta_2=2k_2 d## ##\delta_1-\delta_2=\pi = 4d(\frac{1}{\lambda_1}-\frac{1}{\lambda_2})## ##d=\frac{\lambda_1 \lambda_2}{4 \Delta \lambda}## I have a few issues with doing this 1) i don't know why ##\delta_1-\delta_2=\pi## and 2) when i plot...

Homework Statement An interferometer is illuminated by light from a sodium lamp, which emits two narrow spectral lines at wavelengths of 589.0nm and 589.6nm, with the intensity of the 589.0nm line being twice that of the 589.6nm line. Show that there are values of d at which the visibility of...

Ahh yes! So with the minus sign, does this look right? Thanks

##V=\frac{M}{\rho}## ##\Delta V= \delta \big{(} \frac{1}{\rho_l} + \frac{1}{\rho_s} \big{)}## where ##\delta## is the mass that is converted from solid to liquid. ## \delta= 9.58 \times 10^{-3}## Can we then use ##lM=T\Delta S = \Delta Q## ##\Delta Q = l \delta = 3191.25 J## ? where l is the...

Homework Statement A cylinder is fitted with a piston and is in thermal contact with a heat bath at 273K. Initially the volume in the cylinder is filled with 10kg of pure H2O and about half of this is liquid and the other half is solid. The piston is lowered so as to reduce the volume by 2 ×...

Homework Statement The emission of radiation from the Sun’s disc is observed to peak at 0.5 μm wave- length and that from the Moon’s disc at 10.0μm. A heat engine to power a Moon base is to be constructed using radiation collected from the Sun. What is the maximum theoretical efficiency of such...

I was reading that gyroscopes can be used to measure the angular velocity of precession, such as in the Hubble space telescope, but mathematically how can this be done? Many thanks

Can you solve for N in these, or just plug in values of N?