Quantum Simple Harmonic Oscillator

In summary, the conversation discusses a macroscopic pendulum with a mass of 10 g and a length of 50 cm, and its period of 1.42 s. The ground state energy is computed in part (a) and the quantum number for a state where the mass is raised 0.1 mm above its equilibrium position is determined in part (b). The frequency of motion in this state is also calculated. In part (c), the energies of the excited states are mentioned, along with the increase in energy when the pendulum is raised by 0.1 mm and the corresponding excited-state energy. The correct answer for part (b) is given as 2.1*10^28.
  • #1
jkg
1
0

Homework Statement


The period of a macroscopic pendulum made with a mass of 10 g suspended from
a massless cord 50 cm long is 1.42 s. (a) Compute the ground state (zero-point) energy. (b) If the
pendulum is set into motion so that the mass raises 0.1 mm above its equilibrium position, what will
be the quantum number of this state? (c) What is the frequency of motion in (b)?

Need help! I keep doing the problem but getting the wrong answers. I got A but am not getting B. the answer to B is 2.1*10^28
 
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  • #2
What are the energies of the excited states? By how much does the harmonic oscillator's energy increase when the pendulum is raised 0.1 mm? Which excited-state energy does this correspond to?
 

Related to Quantum Simple Harmonic Oscillator

1. What is a quantum simple harmonic oscillator?

A quantum simple harmonic oscillator is a model used in quantum mechanics to describe the motion of a particle in a potential energy field. It consists of a particle confined to a potential energy well and oscillating back and forth within that well.

2. What is the difference between a classical and quantum simple harmonic oscillator?

In a classical simple harmonic oscillator, the particle follows a continuous and predictable path. In a quantum simple harmonic oscillator, the particle's motion is described by a probability distribution and its exact position and velocity cannot be simultaneously known.

3. How is the energy of a quantum simple harmonic oscillator quantized?

The energy of a quantum simple harmonic oscillator is quantized because the particle's motion is restricted to discrete energy levels. These energy levels are determined by the particle's mass, the strength of the potential energy, and the value of Planck's constant.

4. What is the significance of zero-point energy in a quantum simple harmonic oscillator?

Zero-point energy refers to the minimum energy that a quantum system possesses even at its lowest possible energy state. In a quantum simple harmonic oscillator, the zero-point energy is the lowest possible energy level that the particle can have, even when it is at rest.

5. How is the Schrödinger equation used to describe a quantum simple harmonic oscillator?

The Schrödinger equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system. In the case of a quantum simple harmonic oscillator, the Schrödinger equation is used to calculate the probability of finding the particle at a specific position and time, based on its initial conditions and the properties of the potential energy well.

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