Unformatted text preview: with ~ J characteristic of a scalar observable. (ii) Show that ~ U = ~ V × ~ W is a vector under rotations. 3. Consider an oscillator with a particle of mass m in a quadratic potential with spring constant k . The particle is initially in the ground state when, at t = 0 , the spring constant is suddenly reduced to 1 / 3 of its initial value. Find the probability to f nd the particle in the new ground state immediately after the change in spring constant. 4. Use the variational principle to f nd a lower bound for the ground state energy of a particle con f ned to a 1D potential V ( x ) = V exp ( −  x  /x )....
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 Fall '10
 PaulE.
 Physics, mechanics, ground state, ground state energy, εijk Wk

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