Time independent Schrödinger equation

In summary, the time independent Schrödinger equation can contain either a differentiating 'd' or a differentiating curly 'δ', depending on the number of variables that the wave function psi contains. If psi contains only one variable, then the differentiating symbol is 'd', but if it contains more than one variable, then the symbol is 'δ'. This applies specifically to a 1 dimensional infinite well.
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  • #2
Depends on how many variable will psi contain. If 1, call it x, then it's a d, if more than 1, then it's a [itex] \partial [/itex].
 
  • #3
dextercioby said:
Depends on how many variable will psi contain. If 1, call it x, then it's a d, if more than 1, then it's a [itex] \partial [/itex].

Thanks for that!

The question I am working with relates to a 1 dimensional infinite well.

Therefore in this case it would appear to be just 'd' then.

Thanks again!
 

Related to Time independent Schrödinger equation

1. What is the Time Independent Schrödinger equation?

The Time Independent Schrödinger equation is a fundamental equation in quantum mechanics that describes the behavior of a quantum system in terms of its wave function. It is a second-order partial differential equation that represents the relationship between the energy of a quantum system and its wave function.

2. What is the significance of the Time Independent Schrödinger equation?

The Time Independent Schrödinger equation is significant because it allows us to calculate the energy levels and wave functions of a quantum system. This allows us to make predictions about the behavior and properties of quantum systems, which has important applications in fields such as chemistry, material science, and electronics.

3. How is the Time Independent Schrödinger equation solved?

The Time Independent Schrödinger equation is solved using mathematical techniques such as separation of variables and boundary conditions. These techniques allow us to find the wave function and corresponding energy levels for a given quantum system.

4. What are the limitations of the Time Independent Schrödinger equation?

The Time Independent Schrödinger equation assumes that the potential energy of a system is time-independent, meaning it does not change over time. This is not always the case in real-world systems, so the equation may not accurately describe their behavior.

5. How does the Time Independent Schrödinger equation relate to the uncertainty principle?

The Time Independent Schrödinger equation is one of the fundamental principles in quantum mechanics, which is based on the uncertainty principle. This principle states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously. The Time Independent Schrödinger equation allows us to calculate the probability of finding a particle in a particular position, which is related to the uncertainty principle.

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