Now, if you’re like me and have a hard time understanding complex physics theories, don’t worry.

To kick things off, let’s start with the basics. A classical mechanical oscillator is essentially an object that moves back and forth around its equilibrium position due to a restoring force. Think of a pendulum or a spring on a wall they both have this property. But in quantum mechanics, we add some spice to it!

In QMO, the oscillating particle (let’s say an electron) is described by a wave function that has a certain probability distribution around its equilibrium position. This means that instead of having a definite location like classical particles do, electrons can exist in multiple places at once this is called superposition!

Now, the coolest part: energy levels. In QMO, there are discrete energy levels (called eigenvalues) that an electron can have. These levels correspond to different probability distributions of the wave function around its equilibrium position. The lower the energy level, the more spread out the probability distribution is this means that the electron has a higher chance of being found far away from its equilibrium position.

But here’s where it gets interesting: if we try to measure the position or momentum of an electron in QMO, we can only get certain values (called eigenvalues) that correspond to one of these energy levels! This is called the uncertainty principle essentially, we cannot know both the exact position and momentum of a particle at the same time.

So, let’s say you want to measure the position of an electron in QMO. If you do this measurement, it will collapse the wave function into one of these energy levels (which corresponds to a specific probability distribution). This means that after measuring its position, we can no longer predict where the electron is with certainty instead, we have to use probabilities!

If you want to measure both the position and momentum of an electron in QMO, you cannot do this simultaneously. The reason for this is that measuring one property (like position) will affect the other property (like momentum). This is called quantum entanglement essentially, particles can become linked together so that their properties are dependent on each other!

If you’re still confused, don’t worry this stuff takes time to understand. But the beauty of quantum mechanics is that even though we can’t fully comprehend it all, it has led to some incredible technological advancements (like superconductivity)!

Until next time, keep on oscillating!