Question

What is the difference between semiclassical probability density and classical probability density?

Note: This is for a quantum physics 2 course.

Answer 1

Suppose we have an ensemble of N number of harmonic oscillators. Now if we pick any one of the oscillators then it will have its own energy spectrum, If we know the wave function of this oscillator than by taking we will get the probability of getting nth energy state of that particular oscillator, this is a quantum mechanical probability. Now someone asked us "what is the probability of finding i-th (i-th means out of N oscillator no. " i " oscillator) oscillator in the ground state?". Than here we have to calculate two types of probability out of them one is the probability of picking up i-th oscillator. Here out of N oscillator probability of picking i-th oscillator is (1/N) which is a classical probability and probability that this particle will be in the ground state can be found from his wave function, which is   . So probability that i-th particle will be in ground state is .This probability is called semiclassical probability which is a mixture of classical and quantum mechanical probability.

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