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3. Estimate of time of the universe

Homework Statement Show that the time of matter-radiation equality, t_{eq} can be written: $$t_{eq} =\frac{a_{eq}^{\frac{3}{2}}}{H_{0}\sqrt{\Omega_{m}}} \int_{0}^{1} \frac{x}{\sqrt{x+1}} dx$$ Homework Equations $$t = \int_{0}^{t} dt = \int_{0}^{a} \frac{1}{H(a)} \frac{da}{a}$$ [Given]...
4. Why are unperturbed states valid basis for perturbed system?

Physically, it doesn't necessarily make sense that there isn't an extra state generated by this process? Mathematically - The basis $\{ |\phi_{1}\rangle,|\phi_{2}\rangle \}$ is a valid basis for any state in a Hilbert space $H$ of dimensionality 2. Therefore, so long as I know that...
5. Why are unperturbed states valid basis for perturbed system?

Homework Statement So we have a two state system, with unperturbed eigenstates $|\phi_{1}\rangle$, $|\phi_{2}\rangle$, and Hamiltonian $\mathbf{\hat{H_{0}}}$ - i.e $\mathbf{\hat{H_{0}}}|\phi_{1}\rangle = E_{1}|\phi_{1}\rangle$ We shine some z-polarized light on the system. This...

11. Time Evolution of Operators

Unfortunately, it turns out I got that result as a given from another question- I'm not sure where they derived it from exactly! I've double checked, and they are the same formula, so I'm not sure what to do.
12. Einstein A & B Coefficients

Homework Statement Homework Equations The Attempt at a Solution Very confused by this problem. For one thing, it doesn't specify if there is or isn't any light present to drive the stimulated emission/absorbtion. I guess there's no reason to assume that there is no light - but since the...