How to Estimate Transition Probability

The transition rate, and thus the transition probability, between the initial and final state of a system is related to the amount of coupling between the initial and final state of the system. It's also related to the number of ways in which the transition may occur. In circumstances in which the transition probability is constant over time, it may be estimated using Fermi's golden rule. Fermi's golden rule states that the transition probability is equal to the matrix element squared times the density of the final states times 2 pi divided by h bar.

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Instructions

    • 1

      Calculate the matrix element, which is the coupling between the initial and final states. The matrix element is equal to the integral of the interaction between the initial state wave function and the final state wave function. This interaction is written as "V," so the end of the integral expression should be written as "dv" rather than "dx."

    • 2

      Square the matrix element. In other words, multiply it by itself.

    • 3

      Multiply the product from Step 2 by the density of the final states, which is the number of ways in which the transition may occur.

    • 4

      Multiply the product from Step 3 by 2 pi/(h bar). H bar is h/(2 pi), where "h" is Planck's constant. Thus, 2 pi/(h bar) is equal to 4 pi^2/h. The answer that you get is the transition probability.

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