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hw7 - 6 Quantum Mechanics in One Dimension 6-2(a...

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6 Quantum Mechanics in One Dimension 6-2 (a) Normalization requires 1 2  dx A 2 cos 2 L 4 L 4 2 x L dx A 2 2 1 cos 4 x L L 4 L 4 dx so A 2 L . (b) P 2 0 L 8 dx A 2 cos 2 0 L 8 2 x L dx 4 L 1 2 1 cos 4 x L dx 0 L 8 2 L L 8 2 L L 4 sin 4 x L 0 L 8 1 4 1 2 0.409 6-6 x   A cos kx B sin kx x   kA sin kx kB cos kx 2 x 2   k 2 A cos kx k 2 B sin kx 2 m 2 E U 2 mE 2 A cos kx B sin kx The Schrödinger equation is satisfied if 2 x 2 2 m 2 E U or k 2 A cos kx B sin kx 2 mE A cos kx B sin kx . Therefore E 2 k 2 2 m . 6-9 E n n 2 h 2 8 mL 2 , so E E 2 E 1 3 h 2 8 mL 2
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