Schrodinger Eq. & Energies: Are Values Always Positive?

In summary, the energy values associated with the Schrodinger equation can be positive or negative, but there must be a lowest energy eigenvalue for the system to be stable.
  • #1
oddiseas
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just a question about the energies associted wuth the schrodinger equation> are the energy values always positive values. I thought that since when the eigenfunctions exist the particle is in a bound state, that the energy should be less than that required to escape a bound state and should be negative.
 
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  • #2
oddiseas said:
just a question about the energies associted wuth the schrodinger equation> are the energy values always positive values. I thought that since when the eigenfunctions exist the particle is in a bound state, that the energy should be less than that required to escape a bound state and should be negative.

Yes, the energies can be negative. However, there must exist a lowest energy eigenvalue, otherwise the system could lose an infinite amount of energy.
 
  • #3


Yes, you are correct. In the context of the Schrodinger equation, the energy values are typically negative for bound states and positive for unbound states. This is because the Schrodinger equation is typically used to describe the behavior of particles in a potential well, where the particle is confined to a certain region. In this case, the energy of the particle is lower than the potential energy of the well, resulting in a negative energy value.

However, it is important to note that the energy values in the Schrodinger equation are not always negative for bound states. In some cases, the energy can be positive due to the presence of a repulsive potential or due to the use of a different coordinate system. Additionally, the energy values can also be complex numbers, which can have both positive and negative components.

Overall, the energy values in the Schrodinger equation are not always positive, but they can be positive, negative, or complex depending on the specific system being studied.
 

Related to Schrodinger Eq. & Energies: Are Values Always Positive?

1. What is the Schrodinger Equation?

The Schrodinger Equation is a fundamental equation in quantum mechanics that describes the behavior of a quantum system over time. It is used to calculate the probability of finding a particle at a particular location in space and time.

2. Why are negative energy values not allowed in the Schrodinger Equation?

Negative energy values are not allowed in the Schrodinger Equation because it would result in imaginary solutions, which do not have physical meaning. The Schrodinger Equation is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transformed.

3. Can the Schrodinger Equation predict the exact energy of a quantum system?

No, the Schrodinger Equation can only predict the probability of finding a particle at a particular energy level. The exact energy of a quantum system is uncertain and can only be determined through measurement.

4. How is the Schrodinger Equation related to the concept of superposition?

The Schrodinger Equation allows for the concept of superposition, which is the idea that a particle can exist in multiple states at the same time. This is represented by a wavefunction, which is a mathematical function that describes the probability of a particle being in a particular state.

5. Can the Schrodinger Equation be used for all quantum systems?

The Schrodinger Equation can be used to describe the behavior of particles with wave-like properties, such as electrons, protons, and neutrons. However, it is not applicable to all quantum systems, such as systems with high energies or those that involve interactions with other quantum particles.

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