Why is a QM wave function not normalizable

In summary, a wave function in quantum mechanics is not normalizable if it always has the same sign as its second derivative because it must curve towards the x axis in order to be normalizable. However, this concept does not make sense since a wave function is a complex valued function and cannot be compared using traditional inequality signs.
  • #1
Ed Quanta
297
0
In quantum mechanics, why is a wave function not normalizable if it always has the same sign as its second derivative?
 
Physics news on Phys.org
  • #2
In 1D, if f"/f is positive, the function curves away from the x axis.
To be normalizable, it must in some region curve toward the x axis.
 
  • #3
Ed Quanta said:
In quantum mechanics, why is a wave function not normalizable if it always has the same sign as its second derivative?

Your question doesn't make (too much) sense, since a wave function is a complex (generally with a nonzero imaginary part) valued function and to say that [itex] a+ib >0 [/itex] makes no sense.
 

1. Why is a QM wave function not normalizable?

The normalization condition for a wave function in quantum mechanics requires that the integral of the squared magnitude of the wave function over all space is equal to 1. However, some wave functions may not satisfy this condition, making them non-normalizable.

2. What does it mean for a wave function to be non-normalizable?

A non-normalizable wave function does not have a finite total probability. This means that the probability of finding a particle described by this wave function is not well-defined and cannot be calculated.

3. Can a non-normalizable wave function still describe a physical system?

Yes, in some cases, non-normalizable wave functions can still be used to describe physical systems. For example, in the case of free particles, non-normalizable wave functions can still be used to describe the spread of the wave function over all space.

4. What types of wave functions are typically non-normalizable?

Wave functions that are non-normalizable are typically those that exhibit infinite or unbounded behavior. This can occur in cases such as a particle in an infinite potential well or a wave function that describes a free particle with infinite momentum.

5. How does non-normalizability affect the predictions of quantum mechanics?

Wave functions that are non-normalizable cannot be used to make predictions about the probability of finding a particle in a specific state. In order to make accurate predictions, the wave function must be normalized. However, non-normalizable wave functions can still be used as mathematical tools for understanding the behavior of quantum systems.

Similar threads

  • Quantum Physics
Replies
10
Views
1K
Replies
1
Views
528
Replies
9
Views
801
Replies
3
Views
732
  • Quantum Physics
Replies
21
Views
1K
Replies
8
Views
726
Replies
2
Views
314
  • Quantum Physics
Replies
24
Views
542
Replies
59
Views
3K
  • Quantum Physics
2
Replies
40
Views
3K
Back
Top