Wavefunction Substitution and Momentum

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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?

Momentum Signup and view all the answers

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

Position, momentum, and energy Signup and view all the answers

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

Multiplies the function by a constant Signup and view all the answers

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

Eigenvalue equations Signup and view all the answers

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

By a wavefunction Signup and view all the answers

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

Low mass 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?

The particle overcomes the barrier Signup and view all the answers

What can scanning tunneling microscopy map with high sensitivity?

Atomic heights of a surface Signup and view all the answers

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

$E = Jz2/(2I)$ Signup and view all the answers

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

$\frac{h^2}{8mL^2}$ Signup and view all the answers

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

12 energy levels 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?

The system absorbs blue light Signup and view all the answers

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

The particle reflects Signup and view all the answers

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

It always gives a definite value for momentum. Signup and view all the answers

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

Measurements result in different momentum values based on probabilities. Signup and view all the answers

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

One has positive momentum while the other has negative momentum. Signup and view all the answers

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

They are complementary and cannot be simultaneously specified. Signup and view all the answers

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

It is impossible to specify both position and momentum with arbitrary precision. 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?

The uncertainty in speed increases as the uncertainty in position decreases. Signup and view all the answers