Let |0) and 1) denote the normalized eigenstates corresponding to the ground and first excited states of a one dimensional harmonic oscillator. The uncertainty Ap in the 1 state (0) + |1)), is

Q: A harmonic oscillator is in the state o (3) = N (3² – 3y + 1) exp (-) (a) Expressed the state…

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Q: Consider a linear harmonic oscillator and let vo and i be its real, nor- malized ground and first…

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Q: where and k²-k² = 2m2² (V₂-E) k² = 2 m E I ħ² Show that the solutions for region II can also be…

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Q: calculate the probability of the harmonic oscillator En = (n + 1/2)hcutw is a state with n an odd…

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Q: A harmonic oscillator of mass m and angular frequency w is in the initial state of wavefunction p(x,…

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Q: (4a³ 1/4 T xe-ax²/2, where a = μω ħ The harmonic oscillator eigenfunction ₁(x) = (a) Find (x²) for…

A: Harmonic oscillator eigenfunction Ψ1(x)=(4α3π)1/4 x e-αx2/2                α=μωħ

Q: A quantum gate U performs the following mapping on the Z-basis (standard/computational basis)…

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Q: An atom with total energy 1.84 eV, in a region with no potential energy, is incident on a barrier…

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Q: The wavefunction for a harmonic oscillator with v= 1 is given by: Vv-1 Ny 2y exp 2 Determine the…

A: I have use concept of mean value

Q: A measurement of the magnitude of Sx for the spin 1/2 system produces an eigenvalue

A: There are scalar values called Eigenvalues associated with linear equations in the matrix equations,…

Q: Q#1 Verify Divergence Theorem for F =x?i+zj+ yzk, taken over the cube bounded by x= 0, x = 1, y = 0,…

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Q: A harmonic oscillator is in a state such that a measurement of the energy would yield either (1/2)…

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Q: A ID harmonic oscillator of angular frequency w and charge q is in its ground state at time t=0. A…

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Q: Assume that you have a quantum mechanical observable N with eigenvalues W; and corresponding…

A: The average value of a function (f) of a variable (j) is the sum of all the products of the…

Q: A quantum mechanical particle is confined to a one-dimensional infinite potential well described by…

A: Step 1: Given: Particle in a 1-D infinite potential well described by the potential:V(x) =0,…

Q: Q. A particle is moving in one-dimension that characterized by the state |w) with wave function y«)…

A: Given data,

Q: Let's consider a harmonic oscillator. The total energy of this oscillator is given by E=(p²/2m)…

A: Using energy conservation equation one can write the equation connecting p, x and E and once…

Q: Suppose a harmonic oscillator is subject to a perturbation where zo = Vmw/h is the length scale of…

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Q: Suppose you measure A with eigenvalues A1, 2, and X3 with corresponding eigenvectors |1), |2), and…

A: Solution:   Given that, Normalized wave function (ψ)=α |1>+β|2>+γ|3>

Q: Denoting by [l, m) the eigenvectors of L² and L₂, consider the vector 3 |«b) = √511, −1) + √√³|1,0)…

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Q: Given that, the expectation value of r2 is the inner product (|b}, find the expectation value of…

A: the expectation value of r2 is defined as: <r2> =<ψIr2Iψ>          =∫0∞r2ψ2dV…

Q: A) = e-IAP/2eda" ]0)

A: Coherent states:-Uncertainty productΔx^ΔP^u⩾n+12ℏSo It is going to increase for higher levels. But…

Q: The coherent states la) of a quantum harmonic oscillator are states that minimizes the uncertainty…

A: It is said that,The coherent states  of a quantum harmonic oscillator are states that minimizes the…

Q: (a) Consider the following wave function of Quantum harmonic oscillator: 3 4 V(x, t) =Vo(x)e¯REot…

A: a)   From question So expectation value of x will be, {*since wave function of ground and exited…

Q: angular momentum Lis

A: There are several angular momentum operators, including:Total angular momentum: Usually denoted…

Q: By taking the derivative of the first equation with respect to b, show that the second equation is…

A: We know the ground state of harmonic oscillator are ψ0(x) = mωπℏ14e-mωx22ℏWe know ∆x =…

Q: At what displacements is the probability density a maximum for a state of a harmonic oscillator with…

A: The wavefuntion is: ψ3(x)=N3H3(y)exp-12y2where,…

Q: a simple harmonic oscillator of mass m and angular frequency w is perturbed by additional potential…

A: Given: The perturbed potential is given as V = bx3

Q: e normalization

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Q: The radial function of a particle in a central potential is give by wave r R(r)= A- exp where A is…

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Q: A particle is initially prepared in the state of = 1 = 2, m = −1 >|, a) What's the expectation…

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Q: Legrende polynomials The amplitude of a stray wave is defined by: SO) =x(21+ 1) exp lô] sen ô, P(cos…

A: We have to use property of Legendre polynomial.

Q: calculate the probability of the harmonic oscillator En = (n + 1/2)hw is a state with n an odd…

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Q: Find the result of this indefinite integral of -V In z = In (1 – e #*) p’dp (1 – ap)* -BE If we know…

A: We have to find  the result of this indefinite integral ln z =-Vπ2 ℏ2∫ln(eβE-1) p2(1-αp)4By using…