This set of Engineering Physics Multiple Choice Questions & Answers (MCQs) focuses on “Linearity & Superposition”.
1. The Schrodinger wave equation is _______
c) Differential equation
Explanation: The Schrodinger Wave equation is a linear in the wave function Ψ. It means, that no term has Ψ with a degree greater than 1.
2. If Ψ1 and Ψ2 are two solutions of Schrodinger Wave equation then which of the following is also a solution?
d) Ψ1 + Ψ2
Explanation: Since Schrodinger equation is linear in Ψ, the addition of two solutions of the equation is also a solution of the same equation.
3. Two solutions of Schrodinger Wave equation obey Superposition principle.
Explanation: Schrodinger equation is linear in Ψ. Thus, it has no term with a Ψ of degree more than 1 or a term independent of Ψ. Thus, they would obey superposition principle.
4. The intensity of pattern observed when wave functions are super positioned is similar to ___________
b) Fraunhofer Diffraction
c) Fresnel Diffraction
d) Edge Diffraction
Explanation: The pattern observed when two wave functions superposition, the variation of maximas with minimas is similar to the one observed for the Fraunhofer Diffraction method.
5. The expectation value of which measurement cannot be calculated using the typical method?
Explanation: The expectation value of the momentum cannot be calculated the typical way because, according to the uncertainty principle, no such function as p(x) exist.
6. Wave function do not show interference.
Explanation: As we know, the solution of Schrodinger wave equation obeys the superposition principle. Hence, they can show interference pattern just like light waves.
7. How is information extracted from a wave function?
a) Expectation value
d) Partial differential
Explanation: Once Schrodinger equation has been solved for a particle, the resulting wave functions contains all the information about the particle. This information can be extracted from the wave function by calculating its expectation value.
8. Two operators, α and β, are said to commute when ____________
a) α = β
b) α + β = 0
c) αβ = βα
d) α2 = β2
Explanation: Two operators, α and β, are said to commute when αβ = βα. If the same is not true, then the two operators are not commutable.
9. Any restrictions present on the particle’s motion in a Schrodinger Equation would affect the ___________
Explanation: Any restrictions present on the particle will affect the potential energy function. Once U is known, Schrodinger equation may be solved for the wave function Ψ.
Explanation: The pattern in the below figure is observed when two wave functions from two slits interfere. It is nearly same as the one observed for Diffraction.
Sanfoundry Global Education & Learning Series – Engineering Physics.
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