Unformatted text preview: E < V , how does the decay parameter α depend on E ? If E increases does the wavefunction decay more or less rapidly with distance? 3. Schr¨ odinger’s equation Solve Schr¨ odinger’s equation for the one dimensional step potential V ( x ) = ( if x ≤ V if x > and calculate the reﬂection coeﬃcient. Graph the reﬂection coeﬃcient for 0 < E < 2 V . 4. Electron in a 2-D box a) An electron is inside a two-dimensional box with each side of length a . V = 0 inside the box and V = ∞ outside. Solve Schr¨odinger’s equation and determine the wavefunctions and the formula for the energy levels. b) Calculate the energy of an electron in the 2-D box with sides of length 5 nm for the ground state and the state given by the quantum numbers (3 , 3). List all states with energy equal to or less than the energy of the (3 , 3) state....
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- Fall '10
- Reflection coefficient, 5 nm, energy levels., 1.2 nm, tunnel barrier