Homework Statement
How to calculate the matrix elements of the quantum harmonic oscillator Hamiltonian with perturbation to potential of -2cos(\pi x)
The attempt at a solution
H=H_o +H' so H=\frac{p^2}{2m}+\frac{1}{2} m \omega x^2-2cos(\pi x)
I know how to find the matrix of the normal...
Homework Statement
A pendulum has a length of 0.5m and an amplitude of oscillation of 8 degrees, what is maximum vertical acceleration
Homework Equations
X=Acos(\omega t + \phi)
\omega =\frac{2\pi}{T}
T=2\pi \sqrt{\frac{l}{g}}The Attempt at a Solution
Taking the second derivative with respect...
Ah ok, so:
Tcos\theta=mg (1)
Tsin\theta=m\omega^2R (2)
doing (2)/(1) gives
R=\frac{gtan\theta}{\omega^2}
plugging in the numbers gives 0.036m, is this correct?
Homework Statement
A pendulum is placed on a rotating platform which rotates with angular velocity ω around an axis, at equilibrium the angle between vertical and pendulum is θ
θ= 20 degrees
ω= 10 1/s
how far is the pendulum placed from the axis
Homework Equations...
Ok, then doing the indefinite integral gives v=\sqrt{\frac{2GM}{x}} + C
but I'm not sure about the limits, would it be \frac{1}{2}v^2=-GM\int_{\infty}^{6370}x^{-2}
where 6370 is the radius of the Earth in km?
Thanks
Homework Statement
Assuming the Earth is at rest and alone in the universe what speed would a spaceship arriving at the surface of Earth from an infinitley large distance be if the speed at infinity= 0 and acceleration is caused only by gravity
Homework Equations
F= \frac{GmM}{x^2}...
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