Probability Exercise #2

Please answer the  following questions regarding the Physlet:

 

Start =

End =

Description

Quantum mechanics inherently involves the ideas of probability.  This exercise will test basic ideas regarding the probability density.

Questions

Quantum mechanics inherently involves the idea of probability.  Many of the functions used in quantum mechanics are continuous functions of one variable.  When you click start, one such function will be displayed.  This function will generally be called the probability density, y*(x) y(x), sometimes also denoted as r(x). The probability that an object's position will lie between x and (x + dx) is y*(x) y(x) dx.  For the above function:

  1. Verify that the probability that the object must be somewhere is 1.

  2. Find the probability that the object is located between x = 0.30 and x = 0.32.

  3. Find the probability that the object is located in the left-hand side of the region.

  4. Find the expectation value of x---the probability density is given by 2*sin (pi*x)^2.

  5. Find the standard deviation of the distribution.

You may click here to numerically integrate any function.

Credits

Script by Mario Belloni and Wolfgang Christian.
Questions by Larry Cain and Mario Belloni.
Java applets by Wolfgang Christian