2010 March 19 | Quantum Science Philippines

## Archive for March 19th, 2010

### AN UNDULATORY THEORY OF THE MECHANICS OF ATOMS AND MOLECULES by E. Schrodinger

Friday, March 19th, 2010

EDMAR G. PANTOHAN This report is based on the very interesting researches of L. de Broglie on what he called “phase waves”. The advantages of the wave theory, The laws of motion and quantum condition can be derived from Hamiltonian principle. The discrepancy between the frequency of motion and frequency of emission disappears when the […]

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### Perturbation of a 3-dimensional infinite cubical well

Friday, March 19th, 2010

Karl Patrick S. Casas Consider a three-dimensional infinite cubical well [eq]V(x,y,z)=\left\{ \begin{array} {cccccc} 0, & if &0<x<a,& 0<y<a,& and& 0<z<a \\ \infty, &otherwise& & & & \\ \end{array}[/eq] The stationary states are [eq]\psi^{0}_{n_x,n_y,n_z}(x,y,z)=\left(2/a\right)^{3/2}\sin\left(\frac{n_x \pi}{a}x\right)\sin\left(\frac{n_y \pi}{a}y\right)\sin\left(\frac{n_z \pi}{a}z\right)[/eq] and the allowed ground state energy is given by [eq]E^0_0=3\frac{\pi^2\hbar^2}{2ma^2}[/eq] . The first excited state is triply degenerate, [eq]E^0_1=3\frac{\pi^2\hbar^2}{ma^2}[/eq] […]

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### 2nd-Order Correction

Friday, March 19th, 2010

Rommel J. Jagus Find the 2nd-order correction to the energies [eq](E_n^{2})[/eq] for the potential [eq]H=\alpha \delta (x-\frac{a}{2})[/eq] Solution: [eq] <\Psi_{m}^{0} | H | \Psi_{n}^{0}> = \frac{2} {a} \alpha \int_0^a sin(\frac{m x \pi }{a} ) \delta (x-\frac{a}{2}) sin(\frac{n x \pi }{a})[/eq] [eq] <\Psi_{m}^{0} | H | \Psi_{n}^{0}> =\frac{2} {a} \alpha [a sin(\frac{m \pi }{a} ) sin(\frac{n […]

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