There always exists at least one bound state for any negative attractive potential in one and two dimensions but not always in three dimensions
the verdict
SUPPORTED
the evidence backs this
confidence 85/100
Quantum mechanics dictates that any negative attractive potential in one and two dimensions will always support at least one bound state, whereas in three dimensions a potential must meet certain strength criteria to guarantee a bound state.
Evidence for · 2
Bound states in one and two spatial dimensions
2003 · cited by 43
Paper [0] confirms that an arbitrarily weak attractive potential in one and two spatial dimensions always possesses at least one bound state.
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More for · 1
Sufficient Conditions for an Attractive Potential to Possess Bound States
1965 · cited by 36
Paper [1] discusses the sufficient conditions for an attractive potential to possess bound states across different dimensions, supporting the quantum mechanical principles regarding bound states in lower versus higher dimensions.