Is the ground state of a negative potential always even?

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SUMMARY

The ground state of a negative potential that approaches zero at both positive and negative infinity is even only if the potential itself is even. This conclusion is supported by the properties of quantum mechanics, where the symmetry of the potential directly influences the symmetry of the wave function. The discussion emphasizes that the ground state must be real and devoid of zeros to maintain its even nature.

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OB1
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Is the ground state of any negative potential that goes to zero at + or - infinity always even?
 
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OB1 said:
Is the ground state of any negative potential that goes to zero at + or - infinity always even?

It can be even only if the potential is even too.

But it is real and has no zero's.

AFAIR.
 

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