Download On Spectral Theory for One-Dimensional Schrodinger Operators by Gesztesy F. PDF

By Gesztesy F.

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Our bodies are not equipped with the huge resources they would need to carry out the process of living, in one step, from birth to death. Imagine the size of stomach that would be required to accumulate, all at once, at the very instant of birth, all of the food one will ever need throughout a lifetime, to be used as necessary from day one onwards. Not too practical! So, instead, the human body is anatomically endowed with a “gas tank” (called a stomach) that can be regularly filled and emptied several times a day, every day, throughout one’s lifetime, to provide for nutritional needs.

As we have seen, energy in all its forms vibrates. It has a frequency of vibration, which is the number of cycles per second, determining how that energy is perceived. The unit of measurement for these vibrations is the cycle per second, one cycle per second being called a “hertz” in honor of the German physicist Heinrich R. ” If energy vibrates too fast (beyond ultraviolet light in the electromagnetic spectrum, at around 750–790 million million Hz or higher), humans cannot perceive it at all without technological help in the form of energy-converting transducers.

If, on the other hand, one continues to add energy in the form of a persistent disturbance (a continuous driving function) – such as when one “dribbles” a basketball, or bows a violin string – the affected state, so long as it is able to, continues to vibrate in response to that disturbance. Alternatively (as will be discussed in Chapter 5) the disturbed state of affairs can adjust its PRINCIPLES OF PHYSICS AND THE ELEMENTS OF MUSIC 45 response characteristics to “tolerate” the presence of that disturbance without the need to react to it.

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