Q3:3 A particle is initially represented by a state which is one of the eigenfunctions {o, (x)} of a hamiltonian operator H, namely ø1, whose normalised form is given by 01 (1) = /2exp The eigenvalue for this eigenfunction is 3. (a) What is the mean or average value of r for this state? (b) If the wavefunction of a particle for the above system was instead represented by the normalised state 1 v (x) = (i - Vz) esp (-). exp 271/2 find the probability that a measurement of the energy of the particle yields the eigenvalue 3. ( You may assume that r exp(-x²)dr = Vñ/2.)
Q3:3 A particle is initially represented by a state which is one of the eigenfunctions {o, (x)} of a hamiltonian operator H, namely ø1, whose normalised form is given by 01 (1) = /2exp The eigenvalue for this eigenfunction is 3. (a) What is the mean or average value of r for this state? (b) If the wavefunction of a particle for the above system was instead represented by the normalised state 1 v (x) = (i - Vz) esp (-). exp 271/2 find the probability that a measurement of the energy of the particle yields the eigenvalue 3. ( You may assume that r exp(-x²)dr = Vñ/2.)
Related questions
Question
Transcribed Image Text:Q3:3 A particle is initially represented by a state which is one of the eigenfunctions
{on (x)} of a hamiltonian operator H, namely ø1, whose normalised form is given by
2
ø1 (x) =
1/2texp
The eigenvalue for this eigenfuncțion is 3.
(a) What is the mean or average value of r for this state?
(b) If the wavefunction of a particle for the above system was instead represented by the
normalised state
1
v (x) =
/2m/2 (i – v2r) exp
find the probability that a measurement of the energy of the particle yields the eigenvalue
3.
You may assume that r² exp(-a²)dx = Vñ/2.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 5 images
