Wavefunction Substitution and Momentum

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Questions and Answers

What happens when waves reach a narrow slit?

  • The waves stop propagating.
  • The waves reflect back.
  • The water in the slit vibrates in random directions.
  • The water in the slit vibrates like a point source. (correct)

In which direction are the waves nearly in-phase when arriving at any point?

  • Backward direction
  • Forward direction (correct)
  • Sideways direction
  • Upward direction

What is the fundamental property of matter described as having a joint particle and wave character?

  • Wave interference
  • Maxwell's equations
  • Wave-particle duality (correct)
  • Electron diffraction

What does the wavelength of an electron depend on in quantum mechanics?

<p>Momentum (C)</p> Signup and view all the answers

What does the wave function Ψ(x) in quantum mechanics contain?

<p>Position, momentum, and energy (B)</p> Signup and view all the answers

In quantum mechanics, what does an operator do with a function?

<p>Multiplies the function by a constant (A)</p> Signup and view all the answers

What type of equations are used to find eigenfunctions in quantum mechanics?

<p>Eigenvalue equations (B)</p> Signup and view all the answers

How are physical properties characterized in the new approach to physics mentioned in the text?

<p>By a wavefunction (C)</p> Signup and view all the answers

What characteristic of light particles makes tunneling more significant for them?

<p>Low mass (C)</p> Signup and view all the answers

In the context of tunneling, what happens if the potential energy barrier is larger than the particle's energy?

<p>The particle overcomes the barrier (A)</p> Signup and view all the answers

What can scanning tunneling microscopy map with high sensitivity?

<p>Atomic heights of a surface (B)</p> Signup and view all the answers

Which equation represents the energy of a rotating particle on a ring in classical physics?

<p>$E = Jz2/(2I)$ (A)</p> Signup and view all the answers

What is the energy expression for the lowest energy level (n=1) in the given system?

<p>$\frac{h^2}{8mL^2}$ (B)</p> Signup and view all the answers

For a system with delocalized π electrons, how many energy levels are present?

<p>12 energy levels (A)</p> Signup and view all the answers

What happens when a photon of energy strikes an electron in the system causing a transition from n=11 to n=12?

<p>The system absorbs blue light (A)</p> Signup and view all the answers

How does tunneling behave if the potential energy of a particle does not reach infinity?

<p>The particle reflects (A)</p> Signup and view all the answers

What is a common misconception about the wavefunction Ψ = cos(kx) as mentioned in the text?

<p>It always gives a definite value for momentum. (A)</p> Signup and view all the answers

What is the physical interpretation of the wavefunction being a superposition of two functions?

<p>Measurements result in different momentum values based on probabilities. (A)</p> Signup and view all the answers

How do the momentum values for exp(ikx) and exp(-ikx) differ as discussed in the text?

<p>One has positive momentum while the other has negative momentum. (D)</p> Signup and view all the answers

How does the Heisenberg uncertainty principle relate position and momentum according to the text?

<p>They are complementary and cannot be simultaneously specified. (A)</p> Signup and view all the answers

What does the Heisenberg uncertainty principle state about specifying the properties of particles?

<p>It is impossible to specify both position and momentum with arbitrary precision. (B)</p> Signup and view all the answers

Based on the given text, what does the position-momentum uncertainty relation imply about measuring the speed of an electron?

<p>The uncertainty in speed increases as the uncertainty in position decreases. (C)</p> Signup and view all the answers

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