Q: Suppose that particle in two-dimensional (2D) box a a x; 30 V(xy) = x(а — х) у(b-у) (a³b5)i] Show…
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Q: For a particle in a one-dimensional box, show that the wavefunctions ψ1 and ψ3 are orthogonal.
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Q: 13) Evaluate (p,x) for W1 of a particle-in-a-box.
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Q: 1. Show that wavefunctions in particle in a box are orthonormal
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Q: Suppose a hydrogen atom state was approximated by the function 1s + 2s + 3s where 1s, 2s and 3s are…
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Q: Show that the wave functions ψ2 and ψ3 of a particle in a one-dimensional box are orthogonal.
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Characteristics of a well behaved functions are:
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- For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?Show that the normalization constants for the general form of the wavefunction =sin(nx/a) are the same and do not depend on the quantum number n.What is the degeneracy of an h subshell? An n subshell?
- A particle on a ring has a wavefunction =12eim where equals 0 to 2 and m is a constant. Evaluate the angular momentum p of the particle if p=i How does the angular momentum depend on the constant m?Under what conditions would the operator described as multiplication by i the square root of 1 be considered a Hermitian operator?State whether the following functions are acceptable wavefunctions over the range given. If they are not, explain why not. aF(x)=x2+1,0x10 bF(x)=x+1,x+ cf(x)=tan(x),x d=ex2,x+
- What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?Why does the concept of antisymmetric wavefunctions not need to be considered for the hydrogen atom?Is the uncertainty principle consistent with our description of the wavefunctions of the 1D particle-in-a-box? Hint: Remember that position is not an eigenvalue operator for the particle-in-a-box wavefunctions.
- For an unbound or free particle having mass m in the complete absence of any potential energy that is, V=0, the acceptable one-dimensional wavefunctions are =Aei(2mE)1/2x/h+Bei(2mE)1/2x/h, where A and B are constants and E is the energy of the particle. Is this wavefunction normalizable over the interval x+? Explain the significance of your answer.Describe and justify the Born interpretation of the wavefunction.a) The physical interpretation of the wavefunction and the fact that it is a solution of the Schroedinger equaton, which is a 2nd order differential equation, causes many restrictions on an acceptable wave function solution: (i) it must be single valued; (ii) it must be continuous; (iii) its slope must be continuous; and (iv) it must be normalizable or normalized. Sketch the following functions and check whether they can be wave function. Explain your answers. 1) 4(x) = for 0 < x <∞ 2) Y(x) = | sin(nx)|, for 0 < x< 2 3) Ҹ(x) %3D In (x), for 1 < x < 0o S0 for – 1 < x < 0 (1 for 0SEE MORE QUESTIONS