Please tell me if there are any evidence proving that babies who are ignored during night time if they wake up crying can develop mental problems?

No there is not. You should check your baby and make sure that they are not hungry or have a wet or dirty diaper and that they are not hurt in any way and that they have not thrown up. If not, you can actually help your baby learn to get back to sleep by letting them cry and fuss for a short period of time. .