68110818-3-Problems

68110818-3-Problems - Problems on Postulates, square...

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Problems on Postulates, square potentials, observables and commutators 1. 1st postulates of quantum mechanics state that “ Each physical system is described by a state function which determines all can be known about the system.” What is the fundamental behaviours of the wave function? 2. How can you determine wave function of a quantum particle?(2nd postulate) 3. What is the meaning of correspondence principle? 4. What is the expectation value and eigenvalue of an operator? When they are the same? 5. How can you determine location of a particle? What is the meaning of normalization and orthogonality. 6. Is The following statements true or false (a) The statefunction is always eaual to a function of time multiplied by a function of the coordinates (b) In both classical and quantum mechanics , knowledge of the present state of an isolated system allows its future states to be calculated (c) The statefunction is always an eigenfunction of the Hamiltonian (d) Any linear combination of eigenfunctions of the Hamiltonian is an eigenfunction of the Hamiltonian (e) If the statefunction of is not an eigenfunction of the operator A, then a measurement of the property A might give a value that is not one of the eigenvalues of A (f) The probability density is independent of time for a stationary state (g) If two operators do not commute, then they cannot posses any common eigenfunctions (h) If two operators commute, then every eigenfunction of one must be an eigenfunction of the other (i) If the operator B corresponds to a physical property of a quantum mechanical system, the statefunction must be an eigenfunction of B Answers: (a)F, (b) T. (c) F. (d) F. (e) F. (f) T. (g) F. (h) T (I) F 7. What is the result if the operator apply on the function 8. Show that the function is eigenfunction of .
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This note was uploaded on 01/12/2012 for the course CHEM 133 taught by Professor Staff during the Spring '08 term at UCSD.

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68110818-3-Problems - Problems on Postulates, square...

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