# Question about Schrödinger equation interpretation

• prehisto
In summary, the amplitude of a wave function corresponds to the probability amplitude. The energy of a particle is not related to the amplitude of the wave function.
prehisto

## Homework Statement

Im reading and thinking about the interpretation about Schrödinger equation s solutions (wave functions) - what they really mean.
What does the amplitude of wave function correspond to?
Does it mean that if amplitude is greater then energy of particle is greater as well ?
I would appreciate any help.

## The Attempt at a Solution

prehisto said:
I'm reading and thinking about the interpretation about Schrödinger equation s solutions (wave functions) - what they really mean.
Depends what you mean by "really" ;)
What does the amplitude of wave function correspond to?
It corresponds to the probability amplitude ... it is it's own thing and does not have a physical meaning by itself. You know that the wave-function, along with it's complex conjugate, form the probability density function for the variable concerned. When you start out you normally have position wave-functions.

So ##\psi(x)## is the solution to Schrodinger's equation in x.
##\psi^\star(x)\psi(x)## is the probability density function for the particle in x.
##\int_a^b\psi^\star(x)\psi(x) dx## is the probability of finding the particle with x value between a and b.
Only this last one has a physical meaning ... the rest are steps in a calculation.

Does it mean that if amplitude is greater then energy of particle is greater as well ?
No. The amplitude is related to probability. In general, the energy is related to the number of anti-nodes in the wave-function ... in free-space, that would be proportional to the frequency.

Ok,thanks.
Yes, I was thinkinkg whether the amliptude has a physical interpretation.

Only natural.
It is no more physical than the magnitude of a classical probability density.
Technically it is more abstract than that - being a step removed. Some people find it a bit spooky - that such abstract ideas can have a physical impact. You'll find some people almost view the abstract math has having a deeper reality than the stuff you can measure.

Have a look at:
http://vega.org.uk/video/subseries/8
... for a glimpse of how things work.

The Schrödinger equation is a fundamental equation in quantum mechanics that describes the behavior of particles at the microscopic level. Its solutions, known as wave functions, represent the probability of finding a particle in a certain state at a given time. The amplitude of the wave function corresponds to the square root of the probability density of finding the particle in a particular position. Therefore, a larger amplitude does not necessarily mean a higher energy of the particle. The energy of a particle is determined by the Hamiltonian operator, which acts on the wave function and produces a value known as the expectation value of energy. This value can be different for different states of the particle, regardless of their amplitudes. In summary, the amplitude of a wave function represents the probability of finding a particle in a certain position, not its energy. I hope this helps clarify your understanding of wave function interpretation.

## What is the Schrödinger equation?

The Schrödinger equation is a mathematical equation that describes how the quantum state of a physical system changes with time. It is a fundamental equation in quantum mechanics and is used to calculate the probability of finding a particle at a certain position or energy level.

## What is the interpretation of the Schrödinger equation?

The interpretation of the Schrödinger equation is a subject of debate among scientists. Some interpret it as a description of how the quantum state of a particle evolves over time, while others view it as a statistical description of the behavior of a large number of particles.

## Does the Schrödinger equation apply to macroscopic objects?

The Schrödinger equation is typically used to describe the behavior of subatomic particles and does not directly apply to macroscopic objects. However, some scientists argue that the Schrödinger equation can be extended to describe the behavior of macroscopic objects in certain situations.

## What is the role of the observer in the Schrödinger equation?

The role of the observer in the Schrödinger equation is a topic of controversy in quantum mechanics. Some interpretations of the equation suggest that the observer plays a crucial role in determining the outcome of an experiment, while others argue that the observer is simply a passive observer and does not affect the outcome.

## Are there any alternative interpretations of the Schrödinger equation?

Yes, there are many alternative interpretations of the Schrödinger equation, including the Copenhagen interpretation, many-worlds interpretation, and de Broglie-Bohm interpretation. Each of these interpretations offers a different perspective on the behavior of quantum particles and the role of the observer.

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