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Unformatted text preview: Chem120A Notes 9/5/08 For Particle in a Box: Potential is infinite outside of 0 and a →So, particle can travel from 0 → a (including 0 and a ) →Figure 3.2 from McQuarrie and Simon shows wavefunction and probability density for 1-D Particle in a Box energy levels →Probability density must be positive, as it is 2 ) ( x Ψ Postulates of Quantum Mechanics Postulate 1: “The state of a quantum mechanical system is completely specified by a function Ψ ( x ) that depends upon the coordinate of the particle. All possible information about the system can be derived from Ψ ( x ). This function, called the wavefunction (or state function) has the important property that dx x x ) ( ) ( * Ψ ⋅ Ψ is the probability that the particle lies in the interval dx , located at position x. ” →The maximum number of dimensions a system can have is 3N, where N is the number of particles. Postulate 2: “To every observable in classical mechanics corresponds an operator in quantum mechanics” →Table 4.1 in McQuarrie and Simon shows a list of operators and their corresponding →Table 4....
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