The normalized wave function of a particle in a box in the region -a < x < a is: ?(x) = ?(15 / 16a^5) * (a^2 - x^2) a) Calculate the expectation value of the energy <E> of the particle. b) Calculate the probability of finding the particle in the region 0 ? x ? a
Added by Benjamin R.
Close
Step 1
For a particle in a box, the Hamiltonian operator is given by: H = -ħ^2/2m * d^2/dx^2 where ħ is the reduced Planck's constant and m is the mass of the particle. Show more…
Show all steps
Your feedback will help us improve your experience
Narayan Hari and 57 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The wave function of the particle moving in free space is w(x) = exp(ikx) * exp(-ikx). a) Find the energy of the particle. b) What is the probability current density for the real part of the wave function? The wave function of the particle is given as w(x) = ve. a) Find the probability of the particle in -a < x < a. b) Find the value of b so that the probability of finding the particle in the range -b < x < b is 0.5.
Aarya B.
The wave function for a quantum particle is $$ \psi(x)=\sqrt{\frac{a}{\pi\left(x^{2}+a^{2}\right)}} $$ for $a > 0$ and $-\infty < x < +\infty$ . Determine the probability that the particle is located somewhere between $x=-a$ and $x=+a .$
Luke H.
The wave function for a particle is given by $\psi(x)=A e^{-|x| / a}$ , where $A$ and $a$ are constants. (a) Sketch this function for values of $x$ in the interval $-3 a < x < 3 a$ . (b) Determine the value of $A$ . (c) Find the probability that the particle will be found in the interval $-a < x < a$ .
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD