Use symmetry arguments to show that, in one dimension, if a particle's wavefunction is either even or odd, the average momentum is zero.
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A: Given, L= 1 nm
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A: Given, x=-L2 to x=L2ψ=A sin2πxLA2∫-L2L2sin22πxLdx=1A22∫-L2L21-cos4πxLdxA~2Lwhen, P0.21 L~0.32…
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Q: Find the expectation value of the momentum for the particle in the state, W(x, ) = Ae'lx- wt)
A: Given that ψx,t=Aeikx-ωtψ*x,t=A-ikx-wt ∫ψ*ψ dx =∫Ae-ikx-wtAeikx-ωtdx A2∫dx =1 p=∫-∞∞ ψ*x,t h2πid…
Q: Example (2): Consider a particle whose wave function is given by Þ(x) = Ae-ax.What is the value of A…
A: solution: to find the A for the normalized function.
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A: Given, N10 out of N particles=4E19N10=36 E1
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A: The state of the system is given as
Q: (a) Write the relevant form of Schrödinger equation for the free particle.
A: We have to write relevant form of Schrodinger Equation for the free particle. Note: As question is…
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A: Anharmonic oscillator
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Q: Starting with the time-independent Schrodinger equation, show that = 2m.
A: The time-independent Schrodinger equation is given by: Hψx=EψxH=p22m+u(x)
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A: de-Broglie wavelength: The wave associated with the moving particle is called the de-Broglie wave.…
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A: Introduction: A wave function is defined to be a function describing the probability of a particle's…
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A: We have given potential V(x) =kx for all greater than x.
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A: Given, Wave function of a particle
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A: One harmonic oscilator,
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A: Given Length of the box = 10 nm Wavefunction ψ = 2L12 sin 2πxL
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Q: WHY DOES WAVE - FUNCTION GO TO * INFINITY? THE ZERO AS GOES TO
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- The normalized wavefunction is (1/4*pi*a^2) e^-(x^2)/(2a^2)Particle of mass m moves in a three-dimensional box with edge lengths L1, L2, and L3. (a) Find the energies of the six lowest states if L1 =L, L2 = 2L, and L3 = 2L. (b) Which if these energies are degenerate?Schrodinger equation for the special case of a constant potential energy, equal to U0. Find the general solution of Schrodinger equation when energy of particle E > U0 and when E < U0.
- For the wave function and given N p²+α² p(p) in the momentum space, what is the wave function in position space?A quantum mechanical particle of mass m moves in a 1D potential where a) Estimate the ground state energy of the particle. b) Sketch the wave function to the best of your ability.For the particle in the box in the base state, calculate the quantities <x> and <Px> :