-
Prove the relationship [x,px]=ih
13139 Prove the relationship [x,px]=ih Prove the relationship [x,px]=ih, where px =-ihd/dx. Namely, show that applying the commutator [x,px] to any function f(x) is equal to multiplying ih to f(x).
-
Calculating the commutator of a function with another
1400 Calculating the commutator Find the commutator: [F(x),p]. See attached file for full problem description.
Step 1) Write the expression for the commutator.
Step 2) Consider another function P(x) and let the commutator act on it.
-
Commutator of Wave Function
115968 Commutator of Wave Function Find the commutator of [x , d/dx ] for the wave function described in the attachment.
See attached file for full problem description. Please see the attached file.
-
Operations and Commutator Relationships
We define the commutator of two operators through the expression [A,B] = [A][B] - [B][A].
Prove the following commutator relationships: (a) [x,p] = i^h, (b) [E,t] = i^h, (c) [x,t] = 0, (d) [p,E] = 0.
-
Problem 3.26 in Griffiths' Introduction to Quantum Mechanics
(b) Show that the commutator of two hermitian operators is anti-hermitian. How about the commutator of two anti-hermitian operators?
-
Symmetric and Galois group
(See attached) Notice that [S_3, S_3], the commutator subgroup of S_3, contains (123) = [(12), (13)],
so contains <(123)>, hence has order 3 or 6, by Lagrange.
Observe that any commutator is either equal to the identity
or a 3-cycle.
-
Groups : Symmetry
15975 Groups : Symmetry Note: G' means derived (commutator) subgroup of G and Sn is symmetric group of degree n
Please find G' in each case
(a) G is abelian
(b) G = Sn (a) If G is abelian, then G'={e} since G/G' is isomorphic to G, which is abelian
-
Determine the maximum torque on the shaft.
The loops are connected in parallel to a commutator.
Determine the maximum torque on the shaft if the motor takes a current of 5 A in a uniform flux density of 0.5 T. Please see attached file for the solution to the given problem.
-
Derivation of Virial Theorem in Quantum Mechanics
In a one-dimensional problem, consider a particle with the Hamiltonian:
H = p^2/2m + V(X)
where: V(C) = lambaX^n
Calculate the commutator [H, XP].