Are there any real-life examples of tangent waves in the universe?

[ujellytek]

I'm in high school, just finished Grade 11 and I have learned about sine, cosine, and tangent waves in my math & physics classes. The question is more of where are tangent waves found in nature/this universe? I have thought that maybe electrons experience some sort of tangent wavelike behavior in a quantum leap. Sounds kinda dumb eh? Well I'm thinking this way because in a tangent wave the graphed line keeps and keeps on going (infinitely) and then jumping through the asymptote and appearing below the x-axis of the graph and repeating that (please google the tangent graph if you do not know what it looks like :) ). The relation to this thought with electrons is that when electrons gain enough energy for a quantum leap they jump through a dimension, and then appear in the other energy level of the orbits, sort of like my idea i touched on.

Is this an example of a tangent function like wave in the universe? Does anyone know of a tangent function like wave in the universe?

Also a reason why my idea would not work is because the the electron would have to gain an infinite amount of energy to jump into the other dimension before it appears in the other orbit (like the graph of a tangent function)

 

[Dr. Courtney]

I don't think of tangent like a wave, just as the ratio of sine and cos.

 

[jfizzix]

... The question is more of where are tangent waves found in nature/this universe? I have thought that maybe electrons experience some sort of tangent wavelike behavior in a quantum leap...

...The relation to this thought with electrons is that when electrons gain enough energy for a quantum leap they jump through a dimension, and then appear in the other energy level of the orbits...

...Is this an example of a tangent function like wave in the universe? Does anyone know of a tangent function like wave in the universe?

Congrats on your first post!

Trigonometric functions, like sine, cosine, and tangent are found throughout all branches of physics to be sure. Sine waves are also readily seen because waves oscillating at just one frequency look just like a sine wave.

In fact, all waves can be expressed as a sum of sin waves of different frequencies.

To get a tangent wave in terms of sine waves, you could use the sum:
$tan(x) = 2\big(Sin(2x)-Sin(4x)+Sin(6x)-Sin(8x)+Sin(10x)-Sin(12x)+...\big)$
The problem there is that the sum has an infinite number of terms.

In practice, you couldn't have a true tangent wave in the universe because such a wave would require an infinite amount of energy (higher frequencies require higher energy).
As far as quantum leaps go, quantum mechanics gets exceptionally hard to reason with if you try to imagine electrons as microscopic charged dots that must be in a particular place at any given time.

I'm guessing you're talking about the Bohr model of the atom, where when the electron emits a photon, it leaps down an energy level instantaneously. Indeed, we can use the energy (i.e., frequency) of the photon emitted to tell between what two levels the electron travelled.

The only energy the electron needs to make a quantum leap is an amount equal to the difference between the initial and final energy levels. The electron doesn't need any extra energy for this to occur. The likelihood of a quantum leap happening depends on a number of different factors, but no extra energy is necessary.

 

[ujellytek]

Thank-you for your response jfizzix! You have answered my questions :)