Problem 1.5 | Griffiths' Introduction to Quantum Mechanics | 3rd Edition

Problem 1.5
Consider the wave function Ψ(x, t) = Ae^(−λ|x|)*e^(−iωt) where A, λ, and ω are positive real constants.
(a) Normalize Ψ.
(b) Determine the expectation values of x and x^2.
(c) Find the standard deviation of x. Sketch the graph of |Ψ|^2, as a function of x, and mark the points ({x} + σ) and ({x} − σ), to illustrate the sense in which σ represents the “spread” in x. What is the probability that the particle would be found outside this range?


In this video, we solve Problem 1.5 in Griffiths' Introduction to Quantum Mechanics (3rd Edition) as part of a series of solutions to the textbook's questions.

[Ron-pebp]

Thanks.Subscribed.
At 2:46, instead of splitting to 2 integrals you could keep it 1 integral. Note the integrand is even function of x. So the integral from -inf to +inf is twice the integral from 0 to +inf.

[duncanmarey]

Thank you very much for the amount of effort put into this video!

[rontoolsie]

The Integral for the <x^2> can easily be done the the tabular method of IBP, without using the sneakery of the Feynman technique, which is not as obvious of a method as IBP...but I do appreciate you going over it. Subscribed!

[Ron-pebp]

Be careful with the difference between the magnitude of psi and psi squared - for example at 6:29.
And also z^2 is not |z|^2
If z is complex z^2 is not in general equal to z*z.
And also z^2 is not |z|^2

[arrigofacchini]

I don´t agree with your statement at min 3:20: "all the x values from negative infinity to 0 are negative". They must be all positive since we have the absolute value of x. Still the result is right. Thanks!

[ebtisammuddatherhassoun]

Many thanks!!
in the minute 12 what is the name of the method you used to solve the integral ?in order to practice it more .
or, as third year physics students we are not required to solve these kinds of integrls ?