# Transition Probability

At page 190 of Bransden & Joachain (see the page from http://books.google.com/books?id=i5...nsden,+Charles+Jean+Joachain&hl=da#PPA190,M1"), there are 2 expressions for the transition probability, (4.38) and it's absolute value squared in (4.39).
Is it just me or are the 2 term dimensionally different? Obviously everything from (4.38) is squared in (4.39) except the $d\omega$. Hence they can't be the same dimensionally. How can this be right?

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## Answers and Replies

Cyosis
Homework Helper
I am not sure what the question is, but they are both dimensionless. Probability doesn't have a unit.

Cyosis: Yes they are supposed to be dimensionless, but I just looked at the difference between the 2 expressions.

Note that every term from (4.38) appears squared in (4.39) except for the $d\omega$ term which has the same power in both, hence (4.39) is short by a factor of 1/sec.

In any case (4.38) is not the probability, it's the amplitude.

But it's supposed to be dimensionless like the probability, hence must have the same dimensions.

EDIT:
Ok to make it more clear, then (4.38) has the form

$$c_b = \int_0^{\infty} f(\omega) \, d\omega$$

while (4.39) has the form

$$|c_b|^2 = \int_0^{\infty} |f(\omega)|^2 \, d\omega$$

which certainly can't be right. What's going on?

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Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
That's weird, it certainly does look dimensionally inconsistent, regardless of what cb represents.

I'm assuming ω means what it usually does and has units of s-1.