Virtual Labs

Introduce & explain other cases of inf, fin, and other swe solutions.

1. Explain the difference between an infinite potential well and a finite potential well.

a: An infinite potential well has infinite energy levels, while a finite potential well has finite energy levels. Explanation

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b: An infinite potential well has infinitely high walls, while a finite potential well has walls with finite height. Explanation

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c: An infinite potential well has a continuous spectrum of energy, while a finite potential well has a discrete spectrum. Explanation

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d: An infinite potential well has zero probability of finding a particle outside the well, while a finite potential well has non-zero probability. Explanation

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2. For an electron in an infinite potential well of width \( L \), calculate the energy of the second excited state (n=3).

a: E = 9π^2ħ^2 / 2mL^2 Explanation

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b: E = 6π^2ħ^2 / mL^2 Explanation

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c: E = 3πħ / mL Explanation

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d: E = 9πħ^2 / 2mL Explanation

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3. What does the square of the wave function (|ψ|^2) represent in the context of quantum mechanics?

a: The velocity of the particle. Explanation

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b: The energy of the particle. Explanation

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c: The probability density of finding the particle at a given position. Explanation

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d: The force acting on the particle. Explanation

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4. Given the wave function \( \psi(x) = \sqrt{2/L} \sin(n\pi x/L) \) for a particle in an infinite potential well, what is the probability of finding the particle in the first quarter of the well (0 to L/4) for the ground state (n=1)?

a: 0.25 Explanation

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b: 0.5 Explanation

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c: 0.125 Explanation

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d: 0.75 Explanation

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5. Why is the Schrödinger equation fundamental in quantum mechanics?

a: It describes the energy levels of electrons in atoms. Explanation

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b: It governs the time evolution of a quantum system. Explanation

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c: It explains the wave-particle duality. Explanation

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d: It provides the basis for quantum field theory. Explanation

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