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12:12 AM
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Q: Deriving the differential equation of simple harmonic motion through energy conservation equation

User198When examining the simple undamped harmonic motion of a cart of mass m on a spring with stiffness $k$, we can derive the differential equation of motion using various techniques: Newton's 2nd law, d'Alembert's principle, conservation of energy, Lagrange's equations, etc. I don't understand the "c...

 
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HNQ
5:39 AM
1
Q: Hubbard Model Hamiltonian using Number operator

M tIn Hubbard model one can write Hamiltonian to be, $$\hat{H} = \sum_{ij\sigma} t_{ij} c_{i\sigma}^\dagger c_{j\sigma} + \frac{U_H}{2} \sum_{i} \sum_{\sigma} n_{i\sigma} n_{i,-\sigma}$$ where, $n_{i\sigma} = c_{i\sigma}^\dagger c_{i\sigma}$ is the number operator . Using the anticommutation relatio...

HNQ
HNQ
6:01 AM
1
Q: Would a time-dependent gravitational force be conservative?

BunjiUnder normal circumstances, the gravitational force near Earth's surface, $F_g = mg$ is clearly conservative. You can see this either by noting conceptually that the force is constant and work done by gravity is path-independent, or formally by checking that the curl of the field is zero. What if...


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