Objective
The purpose of this experiment was to study quantum mechanics in classical harmonic oscillator with a simulation.
Experiment
Potential Energy Diagrams
Experiment
Potential Energy Diagrams
Potential energy diagram
1&2.The range of motion is from -5cm to 5cm because the energy the particle is bigger than well in this region.
3. The more time the particle spends in one region, the more likely it is to be detected in that region. The particle spends more time to the left of zero because its kinetic energy (and hence its speed) is much smaller in that region. Therefore, the particle is much more likely to be detected to the left of zero.
4. The turning points move outward from the origin by a factor of the square root of two because 1/2 kx^2 = U
5. The shape of the kinetic energy is a parabola, with the opending down.
6. At the turning point. Because the kinetic energy of the particle at the turning points are zero, it is easier to be detected.
Potential Well
1.
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 is different from finite well.
2.
E = n2 h2 / 8 m L2
= 4 (2.1 MeV)
= 8.4 MeV
No, it is not the energy of the first excited state from finite well.
3. The wavelength of the wavefunction is larger in the finite well than infinite well, because the wavefunction can penetrate into the "forbidden" regions.
1&2.The range of motion is from -5cm to 5cm because the energy the particle is bigger than well in this region.
3. The more time the particle spends in one region, the more likely it is to be detected in that region. The particle spends more time to the left of zero because its kinetic energy (and hence its speed) is much smaller in that region. Therefore, the particle is much more likely to be detected to the left of zero.
4. The turning points move outward from the origin by a factor of the square root of two because 1/2 kx^2 = U
5. The shape of the kinetic energy is a parabola, with the opending down.
6. At the turning point. Because the kinetic energy of the particle at the turning points are zero, it is easier to be detected.
Potential Well
1.
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 is different from finite well.
2.
E = n2 h2 / 8 m L2
= 4 (2.1 MeV)
= 8.4 MeV
No, it is not the energy of the first excited state from finite well.
3. The wavelength of the wavefunction is larger in the finite well than infinite well, because the wavefunction can penetrate into the "forbidden" regions.
4. The energy will decrease. The wavelength of the wavefunction is larger in the finite well than infinite well, so on the same state, the energy of finite well is smaller than infinite well. It shows that as the depth of the well decreases, the energy decreases.
5. The penatrate depth will decrease. As the mass of the particle increases, the chance to penentrate through the forbidden region decreases. Finally, when it is up to a large enough mass, it is consistent with the classical harmonic oscillator in macro scale.
5. The penatrate depth will decrease. As the mass of the particle increases, the chance to penentrate through the forbidden region decreases. Finally, when it is up to a large enough mass, it is consistent with the classical harmonic oscillator in macro scale.
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