Q: Evaluate the commutator [y², 82/8x² +82/8y2] by applying the operators to an arbitrary function f(x,…
A: To calculate the commutator for the operator y2, ∂2∂x2 +∂2∂y2 operating on an arbitrary function…
Q: Which of the following functions are eigenfunctions of the momentum operator? a)eikx, b)eax2, c)x,…
A: Given that, some functions are eikx eax2 x x2 ax+b sin(x+3a) We have to determine among the given…
Q: What are eigen function and eigen values? Explain, whether sinax is an eigen function of the op-…
A:
Q: 3. Show that for the 1-D particle-in-a-box, Y₁ is orthogonal to Y2.
A: The objective of the question is to demonstrate that the wavefunctions Y1 and Y2 of a…
Q: Which of the following functions are eigenfunctions of the operator ·Â if  = d² f(x)/dx²? Check all…
A:
Q: How do the energy eigenstates of the 2D rigid rotor compare to (1) the eigenstates of a free…
A:
Q: can the function x2e-ax^2 be normalized in the range of -inf to inf, and if so what is the…
A: A wavefunction is normalized if:
Q: Use the Laplace transform to solve the system of differntial equations. z+y+z+y y(0) = 1 y-2z y = 0…
A: Step 1: Take the Laplace Transform of Both Equations1.1. Apply Laplace transform to the first…
Q: -ikx +Be an Consider the operators d/dx and d²/dx². Is y(x) = Ae¹kx eigenfunction of these…
A: Eigen function of an operator is that upon operating on a function, produces a constant times the…
Q: Evaluate the integral below between the limits t=0 to t (x=0) (x) Show that A+B → Products -d[A] dt…
A:
Q: If two functions f (x ) and g (x ) are both eigenfunctions of some hermitian operator, what does it…
A: Eigenfunctions are the functions which contains information about the state of the system and which…
Q: Determine the degeneracy of the (3,2,1) energy level where a=b=c.
A:
Q: Determine whether the function f:(-1,00) → R defined by f(x) = 3 x+1-e 3 + x is concave or convex. c…
A: Concave function since it's second derivative is negative alwaysExplanation:Step 1:
Q: Let operator Ĥ. Let be one of the normalized eigenfunctions of a Hamiltonian be an approximation of…
A: The equation given is:Where: is one of the normalized eigenfunctions of the Hamiltonian operator .…
Q: (a) Show whether the operator of the kinetic energy operator K and the momentum operator Px for a…
A: To find out whether the Kinetic energy operator and the momentum operator Px for a one-dimensional…
Q: - Is the function e 2 is an eigen function for the operators (a) (d²/dx²) - x² (b) (1/x)(d/dx). If…
A: (a)Step 1: Compute the first derivative of Step 2: Compute the second derivative ofStep 3: Apply…
Q: If the non-normalized wave function (1-x/b)is e-x/2b, remove the normalized state.
A:
Q: show that ψ2 and ψ3 for the harmonic oscillator are orthogonal
A:
Q: Are the following eigenfunctions of the inversion operator, i, which has the effect of replacing x…
A: Eigen function and eigen value
Q: Say whether the one-dimensional kinetic energy operator (at x) is Hermitic.
A:
Q: Define the term lambda max (λmax)
A: Given that : We have to define lambda max (λmax).
Q: 16. Sketch the piecewise defined function: f(x)= ƒ(x)={² 2 ifx<2 stinital en to rauz 9d -x+4 ifx≥2
A: Piecewise functions are composed of "pieces" of graphs over certain intervals of x, so we shall…
Q: Do the kinetic energy operator and momentum operator commute once they are applied on f(x) =AX?
A:
Q: 2) Write out the operator A² for A = a. d dx +x d b. -2x=+1 c. (B+C) dx Hint: be sure to include an…
A: They are defined as the operations which work on a function to give a relation with an associated…
Q: Find an expression for the indicated set, involving A,B,C, and any of the operations u, n, -…
A: The objective of the question is to find an expression for the set of elements that belong to…
Q: 9) infinite over 7) Provide the formula and interpretation of the principle of wave-particle…
A: Answer: The formula of wave-particle duality is given by
![**P17.20** Evaluate the commutator \([ \hat{x}, \hat{p}_x^2 ]\) by applying the operators to an arbitrary function \(f(x)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78fbc2f9-5ce5-4aa9-99e1-1139be15f6b7%2F96099a00-d3a5-450e-8e4d-04623d0515ed%2Fgfm7jx_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
- P7F.9 In this problem you will establish the commutation relations, given in eqn 7E. 14, between the operators for the x-, y-, and z-components of angular momentum, which are defined in eqn 7F.13. In order to manipulate the operators correctly it is helpful to imagine that they are acting on some arbitrary function f: it does not matter what fis, and at the end of the proof it is simply removed. Consider [,,1,] = ,-11. Consider the effect of the first term on some arbitrary function fand evaluate A D -x dx se The next step is to multiply out the parentheses, and in doing so care needs to be taken over the order of operations. (b) Repeat the procedure for the other term in the commutator, 1,1, f. (c) Combine the results from (a) and (b) so as to evaluate l f-11f;you should find that many of the terms cancel. Confirm that the final expression you have is indeed iħl_f, where l̟ is given in eqn 7F.13. (d) The definitions in eqn 7E.13 are related to one another byDetermine the domain of the function in the correct set notation. f(x)=. 1 2x+6 O {xx ER, x-3} O{xx ER, x#3} O {xx ER, x2} O{xx ER, x=-2}Determine whether the function f:(-1,00) → R defined by f(x) = 3 x+1-e 3 + x is concave or convex. c (a) f: (-1,00)→ R defined by f(x) = 3√√x+1-e-4x + x.
- 4) Is the function = B sin (bx) an eigenfunction of the operator d/dx = = d/dx if B and b are constants and real numbers? Show your work in detail.4. Given these operators A=d/dx and B=x², can you measure the expectation values of the corresponding observables to infinite precision simultaneously?16. Sketch the piecewise defined function: f(x)= ƒ(x)={² 2 ifx<2 stinital en to rauz 9d -x+4 ifx≥2
- Normalize the wave function e-ax in the range 0≤x≤ ∞, with a > 0.Construct the potential energy operator of a particle with potential energy V(x)=1/2kfx2, where kf is a constant(a) Consider a wavefunction of the form: =1+x-1Consider the real part of the spherical harmonic Y2,+2. At which values of ϕ do angular nodes occur? Identify the positions of the corresponding planes. Repeat the process for the imaginary part.3. Plot the eigenstate and particle probability for a particle in a box, with infinite height walls, with n=1, 2, 3, 4 for 0A two-level system is in a quantum state = α₁₁ + a22, which can be represented by the vector a = {a1, a2}. We are looking for the conditions under which is eigenstate of the operator c., defined below. 1) In the expression c.ỗ, c is a vector with components {Cr, Cy, Cz} ( C; are real numbers) and ỗ is a vector with components {σx, σy,σz} (σ¿ are 2 × 2 matrices). This means that the operator c. can also be represented by a 2 × 2 matrix. Write the matrix of the operator c. knowing that 0 0x = = (₁ }) = ( 5 ) . Oy σz= 0 (6-99) 1 0 1 0 2) In matrix form, the eigenvalue equation is AX AX, where A is the matrix of the operator of interest, X the column matrix representing the eigenvector and the corresponding eigenvalue. Write the eigenvalue equa- tion that needs to be verified for the quantum state to be an eigenvector of the operator c.. = 3) Note that AX = XX ⇒ (A - I)X 0, where I is the identity matrix. (AAI)X=0 is true if and only if det(A - I) = 0. Solve this equation for the operator…SEE MORE QUESTIONSRecommended textbooks for youPhysical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,