Question

In: Chemistry

a.Normalize the wavefunction Ψ(x) = 1 in a space of 0 ≤ x ≤ ℓ b....

a.Normalize the wavefunction Ψ(x) = 1 in a space of 0 ≤ x ≤ ℓ

b. Find the probability of finding the particle in the subspace [0,ℓ/2 ]

c. Find the most-likely position of the particle in entire space

d. Find the most-likely position of the particle in the subspace [0,ℓ/3 ]

Solutions

Expert Solution


Related Solutions

Consider the wavefunction Ψ(r,θ,φ) = A(1 – br) exp[-br] a. Show that this wavefunction satisfies the...
Consider the wavefunction Ψ(r,θ,φ) = A(1 – br) exp[-br] a. Show that this wavefunction satisfies the Schroedinger equation for the Hydrogen atom with zero angular momentum. What is its energy eigenvalue? What is b? To what state does this wavefunction correspond? b. Normalize Ψ(r,θ,φ). c. Calculate P( r ). modern physics
Partial differential equation (∂2Ψ/∂x2) – (∂2Ψ/∂y2 ) = 0                       Ψ = Ψ(x,y), i-Find the general...
Partial differential equation (∂2Ψ/∂x2) – (∂2Ψ/∂y2 ) = 0                       Ψ = Ψ(x,y), i-Find the general solution of this partial differential equation by using the separation of variables ii-Find the general solution of this partial differential equation by using the Fourier transform iii-Let Ψ(-L,y) = Ψ(L,y) , and Ψ(x,0) = Ψ(x,L) =0. Write the specific form of the solution you have found in either of part b).
A particle's wave function is ψ(x) = Ae−c(x−b)2 where A = 1.95 nm−1/2 and b =...
A particle's wave function is ψ(x) = Ae−c(x−b)2 where A = 1.95 nm−1/2 and b = 0.600 nm. (a) What is the value of the constant c (in nm−2)? nm−2 (b) What is the expectation value for the position of this particle (in nm)? nm
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms of a. (b) What is the probability to find the particle at x = 0.21a  in a small interval of width 0.01a? (c) What is the probability for the particle to be found between x...
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a , where a and b are positive real constants. (a) Using the normalization condition, find b in terms of a. (b) What is the probability to find the particle at x = 0.33a in a small interval of width 0.01a? (c) What is the probability for the particle to be found...
The parity operator P is defined by ˆ Pψ (x) =ψ (−x) for any function ψ(x)....
The parity operator P is defined by ˆ Pψ (x) =ψ (−x) for any function ψ(x). (a) Prove that this parity operator P is Hermitian. (b) Find its eigenvalues, and also its eigenfunctions (in terms of ψ(x)). (c) Prove that this parity operator commutes with the Hamiltonian when potential V(x) is an even function.
Let X be the space of all continuous functions from [0, 1] to [0, 1] equipped...
Let X be the space of all continuous functions from [0, 1] to [0, 1] equipped with the sup metric. Let Xi be the set of injective and Xs be the set of surjective elements of A and let Xis = Xi ∩ Xs. Prove or disprove: i) Xi is closed, ii) Xs is closed, iii) Xis is closed, iv) X is connected, v) X is compact.
Find the momentum space wavefunction of A/(x^2+a^2). I need detailed, step-by-step explanation.
Find the momentum space wavefunction of A/(x^2+a^2). I need detailed, step-by-step explanation.
Assume that ψ : [a, b] → R is continuously differentiable. A critical point of ψ...
Assume that ψ : [a, b] → R is continuously differentiable. A critical point of ψ is an x such that ψ'(x) = 0. A critical value is a number y such that for at least one critical point x we have y = ψ(x). (a) Prove that the set of critical values is a zero set. (This is the Morse-Sard Theorem in dimension one.) (b) Generalize this to continuously differentiable functions R → R.
Problem 1. At time t = 0 the state of a particle in one dimension (1D) is given by ψ(x, 0) = A x 2 + a 2 Here a and A are some positive constants.
  Problem 1. At time t = 0 the state of a particle in one dimension (1D) is given by ψ(x, 0) = A x 2 + a 2 Here a and A are some positive constants. i) Find A ii) Sketch the graph of the probability density of ψ iii) Find the probability that the particle is within −a < x < a and − √ 2a < x < √ 2a iv) Find the expectation value of the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT