The purpose of this experiment is to explore quantum mechanics in classical harmonic oscillation using a simulator.
Experiment
Potential Energy Diagrams
1. Range: -5cm -- 5cm
2. Because the kinetic energy of the particle is less than the potential energy outside of the well.
3. According to the data, there is a higher probability to detect the particle on the left region because the difference in the particle's kinetic energy and the well potential energy in the left region is smaller than it is on the right region.
4. The turning points move outward from the origin by a factor of radical two because U = (1/2) kx^2
5. The shape of the kinetic energy graph is a concave down parabola
6. At the turning points, because the speed of the particle at that point is 0.
Potential well
E = n2 h2 / 8 m L2
= (1)2 (6.626 x 10-34 J s)2 / 8 (1.673 x 10-27 kg) (10 x 10-15 m)2E = 3.3 x 10-13 J
= 2.1 MeV
No, it's different compared to finite well.
2.
E = n2 h2 / 8 m L2
= 4 (2.1 MeV)
= 8.4 MeV
No, this value is different than the first excited state of the finite well model.
3. The wavelength of the wavefunction is larger in the finite well than it is in the infinite well because the wavefunction in the finite well can penetrate into the "forbidden" regions.
4. The energy will decrease. The wavelength of the wavefunction is larger in the finite well compared to the infinite well, so on the same state, the energy of finite well is smaller than infinite well. As the depth of the well decreases, the energy decreases.5. The penetration depth will decrease. As the mass of the particle increases, the chance to penetrate into the forbidden region decreases. Finally, when it has a large enough mass, it is consistent with the classical harmonic oscillator in macro scale.
The online tutorial helps understand quantum mechanics in classical harmonic oscillator.
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